Stability Analysis of Discrete-Time Switched Linear Time-Varying Systems Based on Function-Dependent LMIs

Abstract

This paper considers the problem of uniformly asymptotic stability (UAS) for discrete-time switched linear time-varying (DSLTV) systems. Starting with discrete-time linear time-varying (DLTV) systems, some stability conditions are given by using function-dependent linear matrix inequalities (LMIs). Comparing with the existing results, the conditions obtained allow the norm and rate of variation of system matrix are unbounded. Furthermore, the obtained results are extended to study the UAS of DSLTV systems, the stability condition is given by combining the methods of function-dependent LMIs with average dwell time. Finally, some further discussions about the relaxation of conditions obtained are also proposed. Three numerical examples are given to illustrate the theoretical results. INDEX TERMS Uniformly asymptotic stability, discrete-time systems, switched systems, linear timevarying systems, function-dependent linear matrix inequalities, average dwell time.

Reachability and Controllability Characterizations for Linear Switched Systems in Discrete Time: A Geometric Approach

“…(11) Proof: Let x(K, x 0 , u(•)) be the solution of (1) at time step k = K with x(0) = x 0 and input sequence u(•) = (u(0), ..., u(K − 1)). Then, from (4) x(K, x 0 , u(•)) = x(K, x 0 , 0) + x(K, 0, u(•)) i.e. x(K, x 0 , u(•)) can be decomposed as the sum of the solution with zero inputs and the solution with zero initial value.…”

“…In applications, there are many physical systems that can be modelled in this framework (see e.g. [1], [2]) and this system class has been attracting many researchers to study its properties such as stability [3], [4], [5] and control designs [6], [7], [8], [9], [10].…”

Singular Switched Systems in Discrete Time: Solvability, Observability, and Reachability Notions

“…This assumption means that (3.1) can be seen as a specially structured time-varying linear system, and there are many physical switched systems that can be modeled in that framework (see e.g. [39,40,41,42,43,44]) and this system class has been attracting many researchers to study its properties such as stability [45,46,47,48] and control designs [49,50,51,52,53].…”