Exponential Stability for Switched Systems with Mixed Time Delays

Abstract

Abstract:The global exponential stability problem for a class of switched systems with mixed time delays is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the exponential stability for our considered systems. Razumikhin-like approach and Leibniz-Newton formula are used to find the stability results. Finally, a numerical example is illustrated to show the improved results from using this method.

Exponential stability analysis and stabilization of switched delay systems

“…First, assume r m = 0, and the maximal upper bound r M are compared for different α. In Table I Table II for Theorem 1 and the result in [44]. From the comparison in Table I and Table II, it is known Theorem 1 is less conservative than results in [44].…”

“…Before proceeding further, the following definitions are preliminarily presented borrowed from [36], [44], [52], [54] for later development.…”

“…The third one is to show the less conservative result in exponential stability analysis for the stabilizing switching law. (1) with two modes and the following parameters borrowed from [44]:…”

“…To name only a few, for the problems of stability analysis, in [42], there are some new results about the delay-independent approach. In [43], the authors present significant results for controller design to guarantee the exponential stability of the systems, and the results are further improved in [44]. On the other hand, in [45], conditions are presented to construct a stabilizing switching signal for constant time delay systems, which are further improved to analyze time-varying delay systems in [46].…”

Further result on H∞ filter design for continuous-time Markovian jump systems with time-varying delay

“…Before proceeding further, we first introduce the following definitions borrowed from [8,13,15], which will be used in the subsequent development.…”