New Results on Model Reduction for Discrete-time Switched Systems with Time Delay

This paper is concerned with the problem of delay-dependent exponential H∞ model reduction for discrete-time switched delay systems under switching signals with average dwell time (ADT). The 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 construct a Lyapunov function for switched delay systems such that ADT approach is used with piecewise Lyapunov matrices instead of common Lyapunov function matrices. Furthermore, sufficient conditions for the solvability of this problem are obtained in terms of strict linear matrix inequalities (LMIs), which lessen the computation complexity. A numerical example is provided to show the effectiveness of the developed method.