Delay-Dependent Exponential H_∞ Criteria for Discrete-Time Switched Delay Systems

Abstract

This chapter is concerned with the problems of delay-dependent exponential H_∞ filtering and model reduction for discrete-time switched delay systems under average dwell time (ADT) switching signals. First, by introducing a proper factor to construct a novel Lyapunov-Krasovskii function and using ADT approach, sufficient conditions for the solvability of exponential H_∞ filtering problem, dependent on the upper and lower bounds of the time-varying delay, are obtained in terms of linear matrix inequalities (LMIs). The second objective is to construct a reduced-order model, which ensures that the resulting error system under switching signal with ADT is exponentially stable with an H_∞ norm bound. A weighting factor α is introduced to present sufficient conditions on the existence of reduced-order model in terms of strict LMIs, which lessen the computation complexity. Two numerical examples are presented to demonstrate the effectiveness of the developed results.