New results on the stability of slowly and fastly cyclic switched linear systems
Tao Sun, Xudong Zhao, Rui Wang
Abstract
In this paper, the stability issue for a class of cyclic switched linear systems with all stable or partly unstable submodes is investigated. Firstly, the new concepts of stable cyclic sequence-dependent cycle dwell time (S-CDT) and unstable cyclic sequence-dependent cycle dwell time (U-CDT) are proposed for the first time. Then, based on linear matrix inequalities (multiple Lyapunov functions) and cycle dwell time (CDT) switching law, the stability conditions for slowly cyclic switched linear (nonlinear) systems with all stable submodes are established. Furthermore, by using linear matrix inequalities (multiple Lyapunov functions), S-CDT and U-CDT switching laws, the stability criteria are derived for slowly and fastly cyclic switched linear (nonlinear) systems with a designed cyclic switching scheme where slow S-CDT switching and fast U-CDT switching are, respectively, applied to partly stable and partly unstable submodes. Finally, three numerical examples are presented to demonstrate the feasibility of the developed results.