Stability analysis and \(H_{\infty}\) model reduction for switched discrete-time time-delay systems. (English) Zbl 1407.93113
Summary: This paper is concerned with the problem of exponential stability and \(H_{\infty}\) 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 \(H_{\infty}\) 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 \(H_{\infty}\) error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93B11 | System structure simplification |
| 93C55 | Discrete-time control/observation systems |
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