Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

In this paper, we investigate the problems of robust delay-dependent ℒ2 gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ2-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.