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[18] R. Hmidi, A. Brahim, F. Hmida, and A. Sellami: Robust fault tolerant control design for nonlinear systems not satisfying matching and minimum phase conditions.*Int. J. Control, Automation and Systems*, 18 (2020), 1–14, DOI:
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[19] H. Rios, D. Efimov, J. Davila, T. Raissi, L. Fridman, and A. Zolghadri: Non-minimum phase switched systems: HOSM based fault detection and fault identification via Volterra integral equation.*Int. J. Adaptive Control and Signal Processing*, 28 (2014), 1372–1397, DOI:
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[20] I. Samy, I. Postlethwaite, and D. Gu: Survey and application of sensor fault detection and isolation schemes.*Control Engineering Practice*, 19 (2011), 658–674, DOI:
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[21] C. Tan and C. Edwards: Sliding mode observers for robust detection and reconstruction of actuator and sensor faults.*Int. J. Robust Nonlinear Control*, 13 (2003), 443–463, DOI:
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[22] C. Tan and C. Edwards: Robust fault reconstruction using multiple sliding mode observers in cascade: development and design.*Proc. 2009 American Control Conf.*, St. Louis, USA, (2009), DOI:
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[23] V. Utkin:*Sliding Modes in Control Optimization*, Berlin: Springer, 1992.

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[25] X. Yan and C. Edwards: Nonlinear robust fault reconstruction and estimation using a sliding modes observer.*Automatica*, 43 (2007), 1605–1614, DOI:
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[26] J. Yang, F. Zhu, and X. Sun: State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers.*Int. J. Adaptive Control and Signal Processing*, 27 (2013), 846–858, DOI:
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[27] A. Zhirabok: Nonlinear parity relation: A logic-dynamic approach.*Automation and Remote Control,* 69 (2008), 1051-1064, DOI:
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[29] A. Zhirabok, A. Shumsky, S. Solyanik, and A. Suvorov: Fault detection in nonlinear systems via linear methods.* Int. J. Applied Mathematics and Computer Science,* 27 (2017), 261–272, DOI:
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[30] A. Zhirabok, A. Zuev, and A. Shumsky: Methods of diagnosis in linear systems based on sliding mode observers.*J. Computer and Systems Sciences Int.,* 58 (2019), 898–914, DOI:
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[31] A. Zhirabok, A. Zuev, andV. Filaretov: Fault identification in underwater vehicle thrusters via sliding mode observers.*Int. J. Applied Mathematics and Computer Science*, 30 (2020), 679–688, DOI:
10.34768/amcs-2020-0050.

Go to article
[2] H. Alwi, C. Edwards, and C. Tan: Sliding mode estimation schemes for incipient sensor faults.

[3] F. Bejarano, L. Fridman, and A. Pozhyak: Unknown input and state estimation for unobservable systems.

[4] F. Bejarano and L. Fridman: High-order sliding mode observer for linear systems with unbounded unknown inputs.

[5] M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki:

[6] A. Brahim, S. Dhahri, F. Hmida, and A. Sellami: Simultaneous actuator and sensor faults reconstruction based on robust sliding mode observer for a class of nonlinear systems.

[7] J. Chan, C. Tan, and H. Trinh: Robust fault reconstruction for a class of infinitely unobservable descriptor systems.

[8] L. Chen, C. Edwards, H. Alwi, and M. Sato: Flight evaluation of a sliding mode online control allocation scheme for fault tolerant control.

[9] M. Defoort, K. Veluvolu, J. Rath, and M. Djemai: Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems.

[10] S. Ding:

[11] C. Edwards and S. Spurgeon: On the development of discontinuous observers

[12] C. Edwards, S. Spurgeon, and R. Patton: Sliding mode observers for fault detection and isolation.

[13] C. Edwards, H. Alwi, and C. Tan: Sliding mode methods for fault detection and fault tolerant control with application to aerospace systems.

[14] V. Filaretov, A. Zuev, A. Zhirabok, and A. Protcenko: Development of fault identification system for electric servo actuators of multilink manipulators using logic-dynamic approach.

[15] T. Floquet, C. Edwards, and S. Spurgeon: On sliding mode observers for systems with unknown inputs.

[16] L. Fridman, A. Levant, and J. Davila: Observation of linear systems with unknown inputs via high-order sliding-modes.

[17] L. Fridman, Yu. Shtessel, C. Edwards, and X. Yan: High-order slidingmode observer for state estimation and input reconstruction in nonlinear systems.

[18] R. Hmidi, A. Brahim, F. Hmida, and A. Sellami: Robust fault tolerant control design for nonlinear systems not satisfying matching and minimum phase conditions.

[19] H. Rios, D. Efimov, J. Davila, T. Raissi, L. Fridman, and A. Zolghadri: Non-minimum phase switched systems: HOSM based fault detection and fault identification via Volterra integral equation.

[20] I. Samy, I. Postlethwaite, and D. Gu: Survey and application of sensor fault detection and isolation schemes.

[21] C. Tan and C. Edwards: Sliding mode observers for robust detection and reconstruction of actuator and sensor faults.

[22] C. Tan and C. Edwards: Robust fault reconstruction using multiple sliding mode observers in cascade: development and design.

[23] V. Utkin:

[24] X. Wang, C. Tan, and G. Zhou: A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions.

[25] X. Yan and C. Edwards: Nonlinear robust fault reconstruction and estimation using a sliding modes observer.

[26] J. Yang, F. Zhu, and X. Sun: State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers.

[27] A. Zhirabok: Nonlinear parity relation: A logic-dynamic approach.

[28] A. Zhirabok, A. Shumsky, and S. Pavlov: Diagnosis of linear dynamic systems by the nonparametric method.

[29] A. Zhirabok, A. Shumsky, S. Solyanik, and A. Suvorov: Fault detection in nonlinear systems via linear methods.

[30] A. Zhirabok, A. Zuev, and A. Shumsky: Methods of diagnosis in linear systems based on sliding mode observers.

[31] A. Zhirabok, A. Zuev, andV. Filaretov: Fault identification in underwater vehicle thrusters via sliding mode observers.

Keywords:
optimal control
aerospace applications
nonlinear systems
mechanical/mechatronics applications
robust control

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Go to article
[2] B. Bidikli, E. Tatlicioglu, E. Zergeroglu, and A. Bayrak: An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics.

[3] B. Bidikli, E. Tatlicioglu, A. Bayrak, and E. Zergeroglu: A new robust integral of sign of error feedback controller with adaptive compensation gain. In

[4] B. Bidikli, E. Tatlicioglu, and E. Zergeroglu: A self tuning RISE controller formulation. In

[5] M. Bouchoucha, M. Tadjine, A. Tayebi, P. Mullhaupt, and S. Bouab- dallah: Robust nonlinear pi for attitude stabilization of a four-rotor miniaircraft: From theory to experiment.

[6] A.E. Bryson and Yu-Chi Ho:

[7] Agus Budiyono and Singgih S. Wibowo: Optimal tracking controller design for a small scale helicopter.

[8] Y.N. Chelnokov, I.A. Pankratov, and Y.G. Sapunkov: Optimal reorientation of spacecraft orbit.

[9] W.-H. Chen, D.J. Ballance, P.J. Gawthrop, and J. O’Reilly: A nonlinear disturbance observer for robotic manipulators.

[10] R. Czyba and L. Stajer: Dynamic contraction method approach to digital longitudinal aircraft flight controller design.

[11] Z.T. Dydek, A.M. Annaswamy, and E. Lavretsky: Adaptive control and the NASA X-15-3 flight revisited.

[12] E.N. Johnson and A.J. Calise: Pseudo-control hedging: a new method for adaptive control. In

[13] H.K. Khalil and J.W. Grizzle:

[14] D.E. Kirk:

[15] L.-V. Lai, C.-C. Yang, and C.-J. Wu: Time-optimal control of a hovering quadrotor helicopter.

[16] J. Leitner, A. Calise, and JV.R. Prasad: Analysis of adaptive neural networks for helicopter flight control.

[17] F.L. Lewis, D. Vrabie, and V.L. Syrmos:

[18] W. MacKunis:

[19] W. MacKunis, P.M. Patre, M.K. Kaiser, and W.E. Dixon: Asymptotic tracking for aircraft via robust and adaptive dynamic inversion methods.

[20] S. Mishra, T. Rakstad, andW. Zhang: Robust attitude control for quadrotors based on parameter optimization of a nonlinear disturbance observer.

[21] R.M. Murray: Recent research in cooperative control of multivehicle systems.

[22] D. Nodland, H. Zargarzadeh, and S. Jagannathan: Neural networkbased optimal adaptive output feedback control of a helicopter UAV.

[23] A. Phillips and F. Sahin: Optimal control of a twin rotor MIMO system using LQR with integral action. In

[24] Federal Aviation Administration. Federal aviation regulations. part 25: Airworthiness standards: Transport category airplanes, 2002.

[25] R.R. Costa, L. Hsu, A.K. Imai, and P. Kokotovic: Lyapunov-based adaptive control ofMIMOsystems.

[26] A.C. Satici, H. Poonawala, and M.W. Spong: Robust optimal control of quadrotor UAVs.

[27] R.F. Stengel:

[28] V. Stepanyan and A. Kurdila: Asymptotic tracking of uncertain systems with continuous control using adaptive bounding.

[29] B.L. Stevens and F.L. Lewis:

[30] I. Tanyer, E. Tatlicioglu, and E. Zergeroglu: A robust adaptive tracking controller for an aircraft with uncertain dynamical terms. In

[31] I. Tanyer, E. Tatlicioglu, and E. Zergeroglu: Neural network based robust control of an aircraft.

[32] I. Tanyer, E. Tatlicioglu, E. Zergeroglu, M. Deniz, A. Bayrak, and B. Ozdemirel: Robust output tracking control of an unmanned aerial vehicle subject to additive state-dependent disturbance.

[33] G. Tao:

[34] Q. Wang and R.F. Stengel: Robust nonlinear flight control of a highperformance aircraft.

[35] H-N. Wu, M-M. Li, and L. Guo: Finite-horizon approximate optimal guaranteed cost control of uncertain nonlinear systems with application to Mars entry guidance.

[36] Q. Xie, B. Luo, F. Tan, and X. Guan: Optimal control for vertical take-off and landing aircraft non-linear system by online kernel-based dual heuristic programming learning.

Keywords:
non integer order systems
heat transfer equation
finite difference
Caputo operator
positive systems

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[26] K. Oprzedkiewicz and W. Mitkowski: A memory-efficient nonintegerorder discrete-time state-space model of a heat transfer process.*International Journal of Applied Mathematics and Computer Science*, 28(4), (2018), 649–659, DOI:
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[27] K. Oprzedkiewicz,W. Mitkowski, E.Gawin, and K. Dziedzic: The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process.*Bulletin of the Polish Academy of Sciences. Technical Sciences,* 66(4), (2018), 501– 507, DOI:
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[28] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Parameter identification for non integer order, state space models of heat plant. In*MMAR 2016: 21th international conference on Methods and Models in Automation and Robotics: 29 August–01 September 2016, Międzyzdroje, Poland*, pages 184– 188, 2016.

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[2] A. Atangana and D. Baleanu: New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer.

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[5] M. Dlugosz and P. Skruch: The application of fractional-order models for thermal process modelling inside buildings.

[6] A. Dzielinski, D. Sierociuk, and G. Sarwas: Some applications of fractional order calculus.

[7] C.G. Gal and M. Warma Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions.

[8] T. Kaczorek Fractional positive contiuous-time linear systems and their reachability.

[9] T. Kaczorek: Singular fractional linear systems and electrical circuits.

[10] T. Kaczorek and K. Rogowski:

[11] A. Kochubei: Fractional-parabolic systems, preprint, arxiv:1009.4996 [math.ap], 2011.

[12] W. Mitkowski: Approximation of fractional diffusion-wave equation.

[13] W. Mitkowski: Finite-dimensional approximations of distributed rc networks.

[14] W. Mitkowski,W. Bauer, and M. Zagorowska: Rc-ladder networks with supercapacitors.

[15] K. Oprzedkiewicz: The discrete-continuous model of heat plant.

[16] K. Oprzedkiewicz: The interval parabolic system.

[17] K. Oprzedkiewicz:Acontrollability problem for a class of uncertain parameters linear dynamic systems.

[18] K. Oprzedkiewicz: An observability problem for a class of uncertainparameter linear dynamic systems.

[19] K. Oprzedkiewicz:Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator.

[20] K. Oprzedkiewicz: Non integer order, state space model of heat transfer process using Atangana-Baleanu operator.

[21] K. Oprzedkiewicz: Positivity problem for the one dimensional heat transfer process.

[22] K. Oprzedkiewicz: Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator.

[23] K. Oprzedkiewicz, K. Dziedzic, and Ł. Wi˛ eckowski: Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator.

[24] K. Oprzedkiewicz and E. Gawin: A non-integer order, state space model for one dimensional heat transfer process.

[25] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Modeling heat distribution with the use of a non-integer order, state space model.

[26] K. Oprzedkiewicz and W. Mitkowski: A memory-efficient nonintegerorder discrete-time state-space model of a heat transfer process.

[27] K. Oprzedkiewicz,W. Mitkowski, E.Gawin, and K. Dziedzic: The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process.

[28] K. Oprzedkiewicz, E. Gawin, and W. Mitkowski: Parameter identification for non integer order, state space models of heat plant. In

[29] P. Ostalczyk:

[30] I. Podlubny:

[31] G. Recktenwald:

[32] M. Rozanski: Determinants of two kinds of matrices whose elements involve sine functions.

[33] N. Al Salti, E. Karimov, and S. Kerbal: Boundary-value problems for fractional heat equation involving caputo-fabrizio derivative.

[34] D. Sierociuk, T. Skovranek, M. Macias, I. Podlubny, I. Petras, A. Dzielinski, and P. Ziubinski: Diffusion process modeling by using fractional-order models.

Keywords:
Navier–Stokes equations
hydrodynamic
approximations
mathematical models
incompressible melt

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Go to article
[2] M.R. Malik, T.A. Zang, and M.Y. Hussaini:Aspectral collocation method for the Navier–Stokes equations.

[3] P.M. Gresho: Incompressible fluid dynamics: some fundamental formulation issues.

[4] R. Lakshminarayana, K. Dadzie, R. Ocone, M. Borg, and J. Reese: Recasting Navier–Stokes equations.

[5] S.Sh. Kazhikenova, S.N. Shaltakov, D. Belomestny, and G.S. Shai- hova: Finite difference method implementation for numerical integration hydrodynamic equations melts.

[6] O.A. Ladijenskaya:

[7] Z.R. Safarova: On a finding the coefficient of one nonlinear wave equation in the mixed problem.

[8] A. Abramov and L.F. Yukhno: Solving some problems for systems of linear ordinary differential equations with redundant conditions.

[9] K. Yasumasa and T. Takahico: Finite-element method for three-dimensional incompressible viscous flow using simultaneous relaxation of velocity and Bernoulli function. 1st report flow in a lid-driven cubic cavity at Re = 5000.

[10] H. Itsuro, Î. Hideki, T. Yuji, and N. Tetsuji: Numerical analysis of a flow in a three-dimensional cubic cavity.

[11] X. Yan, L. Wei, Y. Lei, X. Xue, Y.Wang, G. Zhao, J. Li, and X. Qingyan: Numerical simulation of Meso-Micro structure in Ni-based superalloy during liquid metal cooling.

[12] T.A. Barannyk, A.F. Barannyk, and I.I. Yuryk: Exact Solutions of the nonliear equation.

[13] S. Tleugabulov, D. Ryzhonkov, N. Aytbayev, G. Koishina, and G. Sul- tamurat: The reduction smelting of metal-containing industrial wastes.

[14] S.L. Skorokhodov and N.P. Kuzmina: Analytical-numerical method for solving an Orr–Sommerfeld-type problem for analysis of instability of ocean currents.

[15] N.B. Iskakova, A.T. Assanova, and E.A. Bakirova: Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations.

[16] S.Sh. Kazhikenova, M.I. Ramazanov, and A.A. Khairkulova: epsilon- Approximation of the temperatures model of inhomogeneous melts with allowance for energy dissipation.

[17] J.A. Iskenderova and Sh. Smagulov: The Cauchy problem for the equations of a viscous heat-conducting gas with degenerate density.

[18] A.M. Molchanov:

[19] Y. Achdou and J.-L. Guermond: Convergence Analysis of a finite element projection / Lagrange-Galerkin method for the incompressible Navier–Stokes equations.

[20] M.P. de Carvalho, V.L. Scalon, and A. Padilha: Analysis of CBS numerical algorithm execution to flow simulation using the finite element method.

[21] G. Muratova, T. Martynova, E. Andreeva, V. Bavin, and Z-Q. Wang: Numerical solution of the Navier–Stokes equations using multigrid methods with HSS-based and STS-based smoother.

[22] M. Rosenfeld and M. Israeli: Numerical solution of incompressible flows by a marching multigrid nonlinear method.

5
Synchronization of FitzHugh-Nagumo reaction-diffusion systems via one-dimensional linear control law

Keywords:
FitzHugh-Nagumo
synchronization
uni-dimensional control
linear control
reaction-diffusion system
neuronal networks
Lyapunov’s second method

[1] S.K. Agrawal and S. Das: A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters.
*Nonlinear Dynamics,* 73(1), (2013), 907–919, DOI:
10.1007/s11071-013- 0842-7.

[2] B. Ambrosio and M.A. Aziz-Alaoui: Synchronization and control of coupled reaction–diffusion systems of the FitzHugh–Nagumo type.*Computers & Mathematics with Applications*, 64(5), (2012), 934–943, DOI:
10.1016/j.camwa.2012.01.056.

[3] B. Ambrosio, M.A. Aziz-Alaoui, and V.L.E. Phan: Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type.*Discrete & Continuous Dynamical Systems*, 23(9), (2018), 3787–3797, DOI:
10.3934/dcdsb.2018077.

[4] B. Ambrosio, M. A. Aziz-Alaoui, and V.L.E. Phan: Large time behaviour and synchronization of complex networks of reaction–diffusion systems of FitzHugh–Nagumo type.*IMA Journal of Applied Mathematics, *84(2), (2019), 416–443, DOI:
10.1093/imamat/hxy064.

[5] M. Aqil, K.-S. Hong, and M.-Y. Jeong: Synchronization of coupled chaotic FitzHugh–Nagumo systems.*Communications in Nonlinear Science and Numerical Simulation*, 17(4), (2012), 1615–1627, DOI:
10.1016/j.cnsns. 2011.09.028.

[6] S. Bendoukha, S. Abdelmalek, and M. Kirane: The global existence and asymptotic stability of solutions for a reaction–diffusion system.*Nonlinear Analysis: Real World Applications*. 53, (2020), 103052, DOI:
10.1016/j.nonrwa.2019.103052.

[7] X.R. Chen and C.X. Liu: Chaos synchronization of fractional order unified chaotic system via nonlinear control.*International Journal of Modern Physics B*, 25(03), (2011), 407–415, DOI:
10.1142/S0217979211058018.

[8] D. Eroglu, J.S.W. Lamb, and Y. Pereira: Synchronisation of chaos and its applications.*Contemporary Physics*, 58(3), (2017), 207–243, DOI:
10.1080/00107514.2017.1345844.

[9] R. Fitzhugh: Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations.*The Journal of General Physiology*, 43(5), (1960), 867–896, DOI:
10.1085/jgp.43.5.867.

[10] P.Garcia, A.Acosta, and H. Leiva: Synchronization conditions for masterslave reaction diffusion systems*. EPL*, 88(6), (2009), 60006.

[11] A.L. Hodgkin and A.F. Huxley: A quantitative description of membrane current and its application to conduction and excitation in nerve.*J. Physiol,* 117, (1952), 500–544, DOI:
10.1113/jphysiol.1952.sp004764.

[12] T. Kapitaniak: Continuous control and synchronization in chaotic systems.*Chaos, Solitons & Fractals,* 6 (1995), 237–244, DOI:
10.1016/0960- 0779(95)80030-K.

[13] A.C.J. Luo:*Dynamical System Synchronization*. Springer-Verlag, New York. 2013.

[14] D. Mansouri, S. Bendoukha, S. Abdelmalek, and A. Youkana: On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity.*Applicable Analysis,* 100(3), (2021), 675–694, DOI:
10.1080/00036811.2019.1616694.

[15] F. Mesdoui, A. Ouannas, N. Shawagfeh, G. Grassi, and V.-T. Pham: Synchronization Methods for the Degn-Harrison Reaction-Diffusion Systems.*IEEE Access.,* 8 (2020), 91829–91836, DOI:
10.1109/ACCESS. 2020.2993784.

[16] F. Mesdoui, N. Shawagfeh, and A. Ouannas: Global synchronization of fractional-order and integer-order N component reaction diffusion systems: Application to biochemical models.*Mathematical Methods in the Applied Sciences*, 44(1), (2021), 1003–1012, DOI:
10.1002/mma.6807.

[17] J. Nagumo, S. Arimoto, and S. Yoshizawa: An active pulse transmission line simulating nerve axon.*Proceedings of the IRE*, 50(10), (1962), 2061– 2070, DOI:
10.1109/JRPROC.1962.288235.

[18] L.H. Nguyen and K.-S. Hong: Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions.*Mathematics and Computers in Simulation*, 82(4), (2011), 590–603, DOI:
10.1016/j.matcom. 2011.10.005.

[19] Z.M. Odibat: Adaptive feedback control and synchronization of nonidentical chaotic fractional order systems.*Nonlinear Dynamics*, 60(4), (2010), 479–487, DOI:
10.1007/s11071-009-9609-6.

[20] Z.M. Odibat, N. Corson, M.A. Aziz-Alaoui, and C. Bertelle: Synchronization of chaotic fractional-order systems via linear control.*International Journal of Bifurcation and Chaos*, 20(1), (2010), 81–97, DOI:
10.1142/S0218127410025429.

[21] A. Ouannas, M. Abdelli, Z. Odibat, X. Wang, V.-T. Pham, G. Grassi, and A. Alsaedi:*Synchronization Control in Reaction-Diffusion Systems: Application to Lengyel-Epstein System. Complexity*, (2019), Article ID 2832781, DOI:
10.1155/2019/2832781.

[22] A. Ouannas, Z. Odibat, N. Shawagfeh, A. Alsaedi, and B. Ahmad: Universal chaos synchronization control laws for general quadratic discrete systems.*Applied Mathematical Modelling*, 45 (2017), 636–641, DOI:
10.1016/j.apm.2017.01.012.

[23] A. Ouannas, Z. Odibat, and N. Shawagfeh: A new Q–S synchronization results for discrete chaotic systems.*Differential Equations and Dynamical Systems*, 27(4), (2019), 413–422, DOI:
10.1007/s12591-016-0278-x.

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10.1007/BF02845637.

[25] L.M. Pecora and T.L. Carroll: Synchronization in chaotic systems.*Physical Review Letter,* bf 64(8), (1990), 821–824, DOI:
10.1103/Phys- RevLett.64.821.

[26] M. Srivastava, S.P. Ansari, S.K. Agrawal, S. Das, and A.Y.T. Le- ung: Anti-synchronization between identical and non-identical fractionalorder chaotic systems using active control method.*Nonlinear Dynamics,* 76 (2014), 905–914, DOI:
10.1007/s11071-013-1177-0.

[27] J. Wang, T. Zhang, and B. Deng: Synchronization of FitzHugh–Nagumo neurons in external electrical stimulation via nonlinear control.*Chaos, Solitons & Fractals*, 31(1), (2007), 30–38, DOI:
10.1016/j.chaos.2005.09.006.

[28] J. Wang, Z. Zhang, and H. Li: Synchronization of FitzHugh–Nagumo systems in EES via H1 variable universe adaptive fuzzy control.*Chaos, Solitons & Fractals*, 36(5), (2008), 1332–1339, DOI:
10.1016/j.chaos. 2006.08.012.

[29] L. Wang and H. Zhao: Synchronized stability in a reaction–diffusion neural network model.*Physics Letters A*, 378(48), (2014), 3586–3599, DOI:
10.1016/j.physleta.2014.10.019.

[30] J. Wei and M. Winter: Standingwaves in the FitzHugh-Nagumo system and a problem in combinatorial geometry.*Mathematische Zeitschrift, *254(2), (2006), 359–383, DOI:
10.1007/s00209-006-0952-8.

[31] X. Wei, J.Wang, and B. Deng: Introducing internal model to robust output synchronization of FitzHugh–Nagumo neurons in external electrical stimulation.*Communications in Nonlinear Science and Numerical Simulation*, 14(7), (2009), 3108–3119, DOI:
10.1016/j.cnsns.2008.10.016.

[32] F. Wu, Y. Wang, J. Ma, W. Jin, and A. Hobiny: Multi-channels couplinginduced pattern transition in a tri-layer neuronal network.*Physica A: Statistical Mechanics and its Applications*, 493 (2018), 54–68, DOI:
10.1016/j.physa.2017.10.041.

[33] K.-N. Wu, T. Tian, and L. Wang: Synchronization for a class of coupled linear partial differential systems via boundary control.*Journal of the Franklin Institute*, 353(16), (2016), 4062–4073, DOI:
10.1016/ j.jfranklin.2016.07.019.

Go to article
[2] B. Ambrosio and M.A. Aziz-Alaoui: Synchronization and control of coupled reaction–diffusion systems of the FitzHugh–Nagumo type.

[3] B. Ambrosio, M.A. Aziz-Alaoui, and V.L.E. Phan: Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type.

[4] B. Ambrosio, M. A. Aziz-Alaoui, and V.L.E. Phan: Large time behaviour and synchronization of complex networks of reaction–diffusion systems of FitzHugh–Nagumo type.

[5] M. Aqil, K.-S. Hong, and M.-Y. Jeong: Synchronization of coupled chaotic FitzHugh–Nagumo systems.

[6] S. Bendoukha, S. Abdelmalek, and M. Kirane: The global existence and asymptotic stability of solutions for a reaction–diffusion system.

[7] X.R. Chen and C.X. Liu: Chaos synchronization of fractional order unified chaotic system via nonlinear control.

[8] D. Eroglu, J.S.W. Lamb, and Y. Pereira: Synchronisation of chaos and its applications.

[9] R. Fitzhugh: Thresholds and Plateaus in the Hodgkin-Huxley Nerve Equations.

[10] P.Garcia, A.Acosta, and H. Leiva: Synchronization conditions for masterslave reaction diffusion systems

[11] A.L. Hodgkin and A.F. Huxley: A quantitative description of membrane current and its application to conduction and excitation in nerve.

[12] T. Kapitaniak: Continuous control and synchronization in chaotic systems.

[13] A.C.J. Luo:

[14] D. Mansouri, S. Bendoukha, S. Abdelmalek, and A. Youkana: On the complete synchronization of a time-fractional reaction–diffusion system with the Newton–Leipnik nonlinearity.

[15] F. Mesdoui, A. Ouannas, N. Shawagfeh, G. Grassi, and V.-T. Pham: Synchronization Methods for the Degn-Harrison Reaction-Diffusion Systems.

[16] F. Mesdoui, N. Shawagfeh, and A. Ouannas: Global synchronization of fractional-order and integer-order N component reaction diffusion systems: Application to biochemical models.

[17] J. Nagumo, S. Arimoto, and S. Yoshizawa: An active pulse transmission line simulating nerve axon.

[18] L.H. Nguyen and K.-S. Hong: Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions.

[19] Z.M. Odibat: Adaptive feedback control and synchronization of nonidentical chaotic fractional order systems.

[20] Z.M. Odibat, N. Corson, M.A. Aziz-Alaoui, and C. Bertelle: Synchronization of chaotic fractional-order systems via linear control.

[21] A. Ouannas, M. Abdelli, Z. Odibat, X. Wang, V.-T. Pham, G. Grassi, and A. Alsaedi:

[22] A. Ouannas, Z. Odibat, N. Shawagfeh, A. Alsaedi, and B. Ahmad: Universal chaos synchronization control laws for general quadratic discrete systems.

[23] A. Ouannas, Z. Odibat, and N. Shawagfeh: A new Q–S synchronization results for discrete chaotic systems.

[24] N. Parekh, V.R. Kumar, and B.D. Kulkarni: Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system. Pramana –

[25] L.M. Pecora and T.L. Carroll: Synchronization in chaotic systems.

[26] M. Srivastava, S.P. Ansari, S.K. Agrawal, S. Das, and A.Y.T. Le- ung: Anti-synchronization between identical and non-identical fractionalorder chaotic systems using active control method.

[27] J. Wang, T. Zhang, and B. Deng: Synchronization of FitzHugh–Nagumo neurons in external electrical stimulation via nonlinear control.

[28] J. Wang, Z. Zhang, and H. Li: Synchronization of FitzHugh–Nagumo systems in EES via H1 variable universe adaptive fuzzy control.

[29] L. Wang and H. Zhao: Synchronized stability in a reaction–diffusion neural network model.

[30] J. Wei and M. Winter: Standingwaves in the FitzHugh-Nagumo system and a problem in combinatorial geometry.

[31] X. Wei, J.Wang, and B. Deng: Introducing internal model to robust output synchronization of FitzHugh–Nagumo neurons in external electrical stimulation.

[32] F. Wu, Y. Wang, J. Ma, W. Jin, and A. Hobiny: Multi-channels couplinginduced pattern transition in a tri-layer neuronal network.

[33] K.-N. Wu, T. Tian, and L. Wang: Synchronization for a class of coupled linear partial differential systems via boundary control.

Keywords:
continuous interval systems
Kharitonov polynomials
Routh approximation
modelling
SISO systems
MIMO systems

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[27] A. Abdelhak and M. Rachik: Model reduction problem of linear discrete systems: Admissibles initial states.*Archives of Control Sciences,* 29(1), (2019), 41–55, DOI:
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[30] E.-H. Dulf: Simplified fractional order controller design algorithm.*Mathematics, *7(12), (2019), DOI:
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[31] Y. Menasria, H. Bouras, and N. Debbache: An interval observer design for uncertain nonlinear systems based on the ts fuzzy model.*Archives of Control Sciences*, 27(3), (2017), 397–407, DOI:
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[32] A. Khan, W. Xie, L. Zhang, and Ihsanullah: Interval state estimation for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties.*Archives of Control Sciences*, 29(2), (2019), 289- 305, DOI:
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[33] N. Akram, M. Alam, R. Hussain, A. Ali, S. Muhammad, R. Malik, and A.U. Haq: Passivity preserving model order reduction using the reduce norm method.*Electronics*, 9(6), (2020), DOI:
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[34] K. Kumar Deveerasetty and S. Nagar: Model order reduction of interval systems using an arithmetic operation.*International Journal of Systems Science*, (2020), 1–17, DOI:
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[35] K.K. Deveerasetty,Y. Zhou, S. Kamal, and S.K.Nagar: Computation of impulse-response gramian for interval systems.*IETE Journal of Research,* (2019), 1–15, DOI:
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[36] P. Dewangan, V. Singh, and S. Sinha: Improved approximation for SISO and MIMO continuous interval systems ensuring stability.*Circuits, Systems, and Signal Processing*, (2020), 1–12, DOI:
10.1007/s00034-020-01387-w.

[37] M.S. Kumar, N.V. Anand, and R.S. Rao: Impulse energy approximation of higher-order interval systems using Kharitonov’s polynomials.*Transactions of the Institute of Measurement and Control, *38(10), (2016), 1225–1235, DOI:
10.1177/0142331215583326.

[38] S.K. Mangipudi and G. Begum: A new biased model order reduction for higher order interval systems.*Advances in Electrical and Electronic Engineering*, (2016), DOI:
10.15598/aeee.v14i2.1395.

[39] V.L. Kharitonov: The asymptotic stability of the equilibrium state of a family of systems of linear differential equations.*Differentsial’nye Uravneniya,* 14(11), (1978), 2086–2088.

[40] M. Sharma, A. Sachan and D. Kumar: Order reduction of higher order interval systems by stability preservation approach. In*2014 International Conference on Power, Control and Embedded Systems* (ICPCES), (2014), 1–6.

[41] G. Sastry and P.M. Rao: A new method for modelling of large scale interval systems. IETE Journal of Research, 49(6), (2003), 423–430, DOI: 10.1080/03772063.2003.11416366.

Go to article
[2] A. Gupta, R. Saini, and M. Sharma: Modelling of hybrid energy system— part i: Problem formulation and model development.

[3] S. Singh, V. Singh, and V. Singh: Analytic hierarchy process based approximation of high-order continuous systems using tlbo algorithm.

[4] J. Hu, Y. Yang, M. Jia, Y. Guan, C. Fu, and S. Liao: Research on harmonic torque reduction strategy for integrated electric drive system in pure electric vehicle.

[5] K. Takahashi, N. Jargalsaikhan, S. Rangarajan, A. M. Hemeida, H. Takahashi and T. Senjyu: Output control of three-axis pmsg wind turbine considering torsional vibration using h infinity control.

[6] V. Singh, D.P.S. Chauhan, S.P. Singh, and T. Prakash: On time moments and markov parameters of continuous interval systems.

[7] B. Pariyar and R.Wagle: Mathematical modeling of isolated wind-dieselsolar photo voltaic hybrid power system for load frequency control. arXiv preprint arXiv:2004.05616, (2020).

[8] N. Karkar, K. Benmhammed, and A. Bartil: Parameter estimation of planar robot manipulator using interval arithmetic approach.

[9] F.P.G. Marquez: A new method for maintenance management employing principal component analysis.

[10] F.P.G. Marquez: An approach to remote condition monitoring systems management.

[11] D. Li, S. Zhang, andY. Xiao: Interval optimization-based optimal design of distributed energy resource systems under uncertainties.

[12] A.K. Choudhary and S.K. Nagar: Order reduction in z-domain for interval system using an arithmetic operator.

[13] A.K. Choudhary and S.K. Nagar: Order reduction techniques via routh approximation: a critical survey.

[14] V.P. Singh and D. Chandra: Model reduction of discrete interval system using dominant poles retention and direct series expansion method. In

[15] V. Singh and D. Chandra: Reduction of discrete interval system using clustering of poles with Padé approximation: a computer-aided approach.

[16] Y. Dolgin and E. Zeheb: On Routh-Pade model reduction of interval systems.

[17] S.F. Yang: Comments on “On Routh-Pade model reduction of interval systems”.

[18] Y. Dolgin: Author’s reply [to comments on ‘On Routh-Pade model reduction of interval systems’

[19] B. Bandyopadhyay, O. Ismail, and R. Gorez: Routh-Pade approximation for interval systems.

[20] Y.V. Hote, A.N. Jha, and J.R. Gupta: Reduced order modelling for some class of interval systems.

[21] B. Bandyopadhyay, A. Upadhye, and O. Ismail: /spl gamma/-/spl delta/routh approximation for interval systems.

[22] J. Bokam, V. Singh, and S. Raw: Comments on large scale interval system modelling using routh approximants.

[23] G. Sastry, G.R. Rao, and P.M. Rao: Large scale interval system modelling using Routh approximants.

[24] M.S. Kumar and G. Begum: Model order reduction of linear time interval system using stability equation method and a soft computing technique.

[25] S.R. Potturu and R. Prasad: Qualitative analysis of stable reduced order models for interval systems using mixed methods.

[26] N. Vijaya Anand, M. Siva Kumar, and R. Srinivasa Rao: A novel reduced order modeling of interval system using soft computing optimization approach.

[27] A. Abdelhak and M. Rachik: Model reduction problem of linear discrete systems: Admissibles initial states.

[28] M. Buslowicz: Robust stability of a class of uncertain fractional order linear systems with pure delay.

[29] S.R. Potturu and R. Prasad: Model order reduction of LTI interval systems using differentiation method based on Kharitonov’s theorem.

[30] E.-H. Dulf: Simplified fractional order controller design algorithm.

[31] Y. Menasria, H. Bouras, and N. Debbache: An interval observer design for uncertain nonlinear systems based on the ts fuzzy model.

[32] A. Khan, W. Xie, L. Zhang, and Ihsanullah: Interval state estimation for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties.

[33] N. Akram, M. Alam, R. Hussain, A. Ali, S. Muhammad, R. Malik, and A.U. Haq: Passivity preserving model order reduction using the reduce norm method.

[34] K. Kumar Deveerasetty and S. Nagar: Model order reduction of interval systems using an arithmetic operation.

[35] K.K. Deveerasetty,Y. Zhou, S. Kamal, and S.K.Nagar: Computation of impulse-response gramian for interval systems.

[36] P. Dewangan, V. Singh, and S. Sinha: Improved approximation for SISO and MIMO continuous interval systems ensuring stability.

[37] M.S. Kumar, N.V. Anand, and R.S. Rao: Impulse energy approximation of higher-order interval systems using Kharitonov’s polynomials.

[38] S.K. Mangipudi and G. Begum: A new biased model order reduction for higher order interval systems.

[39] V.L. Kharitonov: The asymptotic stability of the equilibrium state of a family of systems of linear differential equations.

[40] M. Sharma, A. Sachan and D. Kumar: Order reduction of higher order interval systems by stability preservation approach. In

[41] G. Sastry and P.M. Rao: A new method for modelling of large scale interval systems. IETE Journal of Research, 49(6), (2003), 423–430, DOI: 10.1080/03772063.2003.11416366.

Keywords:
planning
conformant planning
conditional planning
parallel planning
uncertainty
linear programming
computational complexity

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Go to article
[2] Ch. Backstrom: Computational Aspects of Reordering Plans.

[3] Ch. Baral, V. Kreinovich, and R. Trejo: Computational complexity of planning and approximate planning in the presence of incompleteness.

[4] R. Bartak: Constraint satisfaction techniques in planning and scheduling: An introduction.

[5] A. Bhattacharya and P. Vasant: Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP,

[6] J. Blythe: An Overview of Planning Under Uncertainty.

[7] T. Bylander: The Computational Complexity of Propositional STRIPS Planning.

[8] T. Bylander: A Linear Programming Heuristic for Optimal Planning. In

[9] L.G. Chaczijan: A polynomial algorithm for linear programming.

[10] E.R. Dougherty and Ch.R. Giardina:

[11] I. Elamvazuthi, P. Vasant, and T. Ganesan: Fuzzy Linear Programming using Modified Logistic Membership Function,

[12] A. Galuszka: On transformation of STRIPS planning to linear programming.

[13] A. Galuszka, W. Ilewicz, and A. Olczyk: On Translation of Conformant Action Planning to Linear Programming.

[14] A. Galuszka, T. Grzejszczak, J. Smieja, A. Olczyk, and J. Kocerka: On parallel conformant planning as an optimization problem.

[15] M. Ghallab et al.:

[16] A. Grastien and E. Scala: Sampling Strategies for Conformant Planning.

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[19] J. Koehler and K. Schuster:

[20] R. van der. Krogt: Modification strategies for SAT-based plan adaptation.

[21] M.D. Madronero, D. Peidro, and P. Vasant: Vendor selection problem by using an interactive fuzzy multi-objective approach with modified s-curve membership functions.

[22] A. Nareyek, C. Freuder, R. Fourer, E. Giunchiglia, R.P. Goldman, H. Kautz, J. Rintanen, and A. Tate: Constraitns and AI Planning.

[23] N.J. Nilson:

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[25] D. Peidro and P. Vasant: Transportation planning with modified scurve membership functions using an interactive fuzzy multi-objective approach,

[26] F. Pommerening, G. Roger, M. Helmert, H. Cambazard, L.M. Rousseau, and D. Salvagnin: Lagrangian decomposition for classical planning.

[27] T. Rosa, S. Jimenez, R. Fuentetaja, and D. Barrajo: Scaling up heuristic planning with relational decision trees.

[28] S.J. Russell and P. Norvig:

[29] J. Seipp, T. Keller, and M. Helmert: Saturated post-hoc optimization for classical planning.

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[33] X. Zhang, A. Grastien, and E. Scala: Computing superior counterexamples for conformant planning.

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Keywords:
null-controllability
mobile control
nonlinear constraints
triangular wave
rectangular wave
Green’s function approach
heuristic control
lack of exact controllability

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[2] S.A. Avdonin and S.A. Ivanov:

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[2] A. O’Dwyer:

[3] A.R. Pathiran and J. Prakash: Design and implementation of a modelbased PI-like control scheme in a reset configuration for stable single-loop systems.

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[10] I.L. Chien: IMC-PID controller design-an extension.

[11] J. Lee and T.F. Edgar: Improved PI controller with delayed or filtered integral mode.

[12] J. Na, X. Ren, R. Costa-Castello, and Y. Guo: Repetitive control of servo systems with time delays.

[13] J.E. Normey-Rico, C. Bordons and E.F. Camacho: Improving the robustness of dead-time compensating PI controllers.

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**If the manuscript is not prepared with TeX**, mathematical expressions should be carefully written so as not to arouse confusion. Care should be taken that subscripts and superscripts are easily readable.

**Tables and figures** should be placed as desired by the Author within the text or on separate sheets with their suggested location indicated by the number of table or figure in the text. Figures, graphs and pictures (referred to as Fig. in the manuscript) should be numbered at the beginning of their caption following the figure. All figures should be prepared as PostScript EPS files or LaTeX picture files; in special cases, bitmaps of figure are also acceptable. The numbers and titles of tables should be placed above the main body of each table.

**References** should be listed alphabetically at the end of the manuscript. They should be numbered in ascending order and the numbers should be inserted in square brackets. References should be organized as follows. First initial(s), surname(s) of the author(s) and title of article or book. Then, for papers: title of periodical or collective work, volume number (year of issue), issue number, and numbers of the first and the last page; for books: publisher's name(s), place and year of issue. Example:

- R. E. Kalman: Mathematical description of linear dynamical system. SIAM J. Control. 1(2), (1963), 152-192.
- F. C. Shweppe: Uncertain dynamic systems. Prentice-Hall, Englewood Cliffs, N.J. 1970.

Please, give full titles of journals; only common words like Journal, Proceedings, Conference, etc. may be abbreviated ( to J., Proc., Conf., ... respectively). References to publications in the body of the manuscript should be indicated by the numbers of the adequate references in square brackets. When the paper is set in TeX the preferable form of preparing references is Bib TeX bib database.

**Footnotes** should be placed in the manuscript, beginning with "Received..." (date to be filled in by Editor), the author's institutional affiliation and acknowledgement of financial support,