TY - JOUR
N2 - Positively invariant sets play an important role in the theory and applications of dynamical systems. The stability in the sense of Lyapunov of the equilibrium x = 0 is equivalent to the existence of the ellipsoidal positively invariant sets. The constraints on the state and control vectors of dynamical systems can be formulated as polyhedral positively invariant sets in practical engineering problems. Numerical checking method of positive invariance of polyhedral sets is addressed in this paper. The validation of the positively invariant sets can be done by solving LPs which can be easily done numerically. It is illustrated by examples that our checking method is effective. Compared with the now existing algebraic methods, numerical checking method is an attractive method in that it’s easy to be implemented.
L1 - http://so.czasopisma.pan.pl/Content/116288/PDF/21_593-599_01490_Bpast.No.68-3_30.06.20_KG_TeX.pdf
L2 - http://so.czasopisma.pan.pl/Content/116288
PY - 2020
IS - 31
EP - 599
DO - 10.24425/bpasts.2020.133110
KW - positively invariant set
KW - linear system
KW - polyhedral set
KW - polyhedral cone
KW - linear programming
A1 - Yang, H.
A1 - Hu, Y.
VL - 68
DA - 30.06.2020
T1 - Numerical checking method for positive invariance of polyhedral sets for linear dynamical systems
SP - 593
UR - http://so.czasopisma.pan.pl/dlibra/publication/edition/116288
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -