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This paper is concerned with the problem of exponential stability andH∞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 withH∞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 anH∞error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.

The switching signal design for exponential stability with ${H}_{\infty }$ performance of uncertain switched linear discrete-time systems with interval time-varying delay is considered. Systems with norm-bounded parameter uncertainties are considered. By taking a new Lyapunov-Krasovskii (LK) function, sufficient conditions for the existence of a class of stabilizing switching laws are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered switched time-delay system to be exponentially stable. The resulting stability criteria are of fewer matrix variables and are less conservative than some existing ones. In addition, numerical examples are illustrated to show the main improvement.