Switching design for exponential stability of a class of nonlinear hybrid time-delay systems

Generalized Lyapunov function theorems and its applications in switched systems

“…The results of [5,10,16], based on some stable convex combinations technique and extended MLFs method, present a state-dependent switching law which makes switched systems with unstable modes exponentially (asymptotically) stable. Unlike them, Theorem 4 (resp., Theorem 5) of this paper, obtained by GLF theory (resp., ADT approach), gives a class of state-independent switching signals.…”

“…In spite of their apparent simplicity, switched systems present a very complicated dynamical behaviors due to the multiple subsystems and various possible switching signals. For a large decade, the investigations of stability and stabilization for switched systems have attracted a growing attention in Systems Engineering and Computer Sciences communities, and fruitful results have been reported [5,6,[9][10][11][12][13][14][15][16][17][18][19][20][21][22]. It is well known that ensuring independently stability for each mode of switched systems does not necessarily lead to global stability.…”

“…To investigate this problem, the multiple Lyapunov functions (MLFs) [5,[10][11][12][13][14][15][16][17] and polytopic quadratic Lyapunov functions (PQLFs) [18,19] method were proposed, both of which are nontraditional Lyapunov functions. The reason for considering MLFs and PQLFs is that common Lyapunov function (CLF) does not exist for some switched systems.…”

Stability and stabilization of switched linear discrete-time systems with interval time-varying delay

“…A switched system with time-delay individual subsystems is called a switched time-delay system; in particular, when the subsystems are linear, it is then called a switched time-delay linear system. During the past decades, the stability analysis of switched linear continuous/discrete time-delay systems has attracted a lot of attention [4][5][6][7][8]. The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and linear matrix inequality (LMI) approach for constructing a common Lyapunov function [9][10][11].…”

Switching signal design for stability of switched systems with time-varying delay

“…Some examples for switched systems are automated highway systems, constrained robotics, power systems and power electronics, transmission and stepper motors [5][6]. Stability of switched time-delay systems has been an attractive research topic which is composed of subsystems with their own parameterizations [6][7][8][9][10][11][12][13][14][15]. It is interesting to note that the stability for each subsystem cannot imply that of the overall system under arbitrary switching signal [10].…”