### Details

#### Title

An improvement of Gamma approximation for reduction of continuous interval systems#### Journal title

Archives of Control Sciences#### Yearbook

2021#### Volume

vol. 31#### Issue

No 2#### Affiliation

Bokam, Jagadish Kumar : Department of Electrical Electronics and Communication Engineering, Gandhi Institute of Technology and Management (Deemed to be University), Visakhapatnam, 530045, Andhra Pradesh, India ; Singh, Vinay Pratap : Department of Electrical Engineering, Malaviya National Institute of Technology Jaipur, India ; Devarapalli, Ramesh : Department of Electrical Engineering, BITSindri, Dhanbad, Jharkhand ; Márquez, Fausto Pedro García : Ingenium Research Group, University of Castilla-La Mancha, Spain#### Authors

#### Keywords

continuous interval systems ; Kharitonov polynomials ; Routh approximation ; modelling ; SISO systems ; MIMO systems#### Divisions of PAS

Nauki Techniczne#### Coverage

347-373#### Publisher

Committee of Automatic Control and Robotics PAS#### Bibliography

[1] A.S.S. Abadi, P.A. Hosseinabadi, S.Mekhilef and A. Ordys: A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems.*Archives of Control Sciences*, 30(3), (2020), 599–620, DOI: 10.24425/acs.2020.134679.

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

*Renewable Energy,*36(2), (2011), 459–465, DOI: 10.1016/j.renene.2010.06.035.

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

*International Journal of Dynamics and Control,*7(1), (2019), 53–60, DOI: 10.1504/IJSCC.2020.105393.

[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.

*Electronics,*9(8), (2020), DOI: 10.3390/electronics9081241.

[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.

*Energies,*13(13), (2020), DOI: 10.3390/en13133474.

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

*Journal of Circuits, Systems and Computers*, 26(3), (2017), DOI: 10.1142/S0218126617500384.

[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.

*Arabian Journal for Science and Engineering*, 39(6), (2014), 5289–5295, DOI: 10.1007/s13369-014-1199-z.

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

*Structural Durability & Health Monitoring,*6(2), (2010), DOI: 10.3970/sdhm.2010.006.089.

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

*IET International Conference on Railway Condition Monitoring,*(2006), 156–160, DOI: 10.1049/ic:20060061.

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

*Energies,*13(13), (2020), DOI: 10.3390/en13133465.

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

*Circuits, Systems, and Signal Processing*, 38(3), (2019), 1023–1038, DOI: 10.1007/s00034-018-0912-7.

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

*IETE Journal of Research,*65(3), (2019), 365–379, DOI: 10.1080/03772063.2017.1419836.

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

*5th International Power Engineering and Optimization Conference*, (2011), 27– 30, DOI: 10.1109/PEOCO.2011.5970421.

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

*International Journal of Engineering, Science and Technology*, 4(1), (2012), 97–105, DOI: 10.4314/ijest.v4i1.11S.

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

*IEEE Transactions on Automatic Control*, 48(9), (2003), 1610–1612, DOI: 10.1109/TAC.2003.816999.

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

*IEEE Transactions on Automatic Control,*50(2), (2005), 273– 274, DOI: 10.1109/TAC.2004.841885.

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

*. IEEE Transactions on Automatic Control,*50(2), (2005), 274–275, DOI: 10.1109/TAC.2005.843849.

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

*IEEE Transactions on Automatic Control,*39(12), (1994), 2454–2456, DOI: 10.1109/9.362850.

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

*International Journal of Modelling and Simulation,*34(2), (2014), 63–69, DOI: 10.2316/Journal.205.2014.2.205-5785.

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

*IEEE Transactions on Automatic Control,*42(8), (1997), 1127–1130, DOI: 10.1109/9.618241.

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

*Journal of Advanced Research in Dynamical and Control Systems*, 9(18), (2017), 1571–1575.

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

*Electronics Letters*, 36(8), (2000), 768–769, DOI: 10.1049/el:20000571.

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

*Advances in Electrical and Electronic Engineering*, 14(2), (2016), 153– 161, DOI: 10.15598/aeee.v14i2.1432.

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

*IETE Journal of Research*, (2018), 1–9, DOI: 10.1080/03772063.2018.1528185.

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

*Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering*, 232(7), (2018), 879–894, DOI: 10.1177/0959651818766811.

[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: 10.24425/acs.2019.127522.

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

*Archives of Control Sciences*, 25(2), (2015), 177–187.

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

*IETE Journal of Research*, (2019), 1–17, DOI: 10.1080/03772063.2019.1686663.

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

*Mathematics,*7(12), (2019), DOI: 10.3390/math7121166.

[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: 10.1515/acsc-2017-0025.

[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: 10.24425/acs.2019.129383.

[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: 10.3390/electronics9060964.

[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: 10.1080/00207721.2020.1746433.

[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: 10.1080/03772063.2019.1690592.

[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.