Stability Analysis and Model Reduction for Switched Discrete-Time Time-Delay Systems

This paper is concerned with the problem of exponential stability and model reduction of a class of switched discrete-time systems with state time-varying delay. Some subsystems can be unstable. Based on the average dwell time technique and Lyapunov-Krasovskii functional (LKF) approach, sufficient conditions for exponential stability with performance of such systems are derived in terms of linear matrix inequalities (LMIs). For the high-order systems, sufficient conditions for the existence of reduced-order model are derived in terms of LMIs. Moreover, the error system is guaranteed to be exponentially stable and an error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.

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