Quasi-time-dependent H_∞ Control for Discrete-time Switched Systems With Time-varying Delay and Unstable Modes

The issues of stability, l₂-gain analysis and H_∞ control are addressed for a class of discrete-time switched systems subject to time-varying delay and unstable modes in this paper. To solve the problems, firstly, a hybrid mode-dependent average dwell time (HMDADT) switching strategy is designed by combining slow/fast switching strategy to cope with stable and unstable modes. And improved reciprocally convex combination inequality method is adopted to deal with time-varying delay. Then, by constructing a quasi-time-dependent (QTD) Lyapunov-Krasovskii functional (LKF) with triple sum, new sufficient criteria for global uniform asymptotic stability and l₂-gain analysis of the constructed systems are presented. Moveover, based on the above results, a set of QTD H_∞ controllers are designed to ensure that the corresponding closed-loop system is globally uniformly asymptotically stable (GUAS) with a prescribed weighted H_∞ performance. The QTD controllers designed in this paper are less conservative than the time-independent ones. Finally, two examples are carried out to demonstrate the effectiveness and validity of the developed results.