TY - JOUR
T1 - A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
AU - Rubagotti, Matteo
AU - Zaccarian, Luca
AU - Bemporad, Alberto
N1 - Publisher Copyright:
© 2015 Taylor & Francis.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/5/3
Y1 - 2016/5/3
N2 - This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
AB - This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
KW - Hybrid systems
KW - piecewise-affine systems
KW - stability analysis
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U2 - 10.1080/00207179.2015.1108456
DO - 10.1080/00207179.2015.1108456
M3 - Article
AN - SCOPUS:84958766459
VL - 89
SP - 950
EP - 959
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 5
ER -