Quasi-time-dependent robust \(\mathcal{H}_\infty\) static output feedback control for uncertain discrete-time switched systems with mode-dependent persistent dwell-time. (English) Zbl 1450.93013
Summary: This paper is concerned with the problem of robust \(\mathcal{H}_\infty\) static output feedback control for a class of uncertain discrete-time switched systems under mode-dependent persistent dwell-time (MPDT) switching scheme. The interested systems are described by the classical polytopic-type uncertain model with time-varying parametric uncertainties. The purpose of this paper is to design a static output feedback controller that ensures the resulting closed-loop system robustly globally uniformly asymptotically stable (GUAS) with a specified \(\mathcal{H}_\infty\) performance under MPDT switching. By using a quasi-time-dependent (QTD) and parameter-dependent switched Lyapunov-like function suitable to MPDT switching, the sufficient conditions for stability criterion and \(\mathcal{H}_\infty\) performance analysis are established. Furthermore, a set of QTD switched static output feedback controllers for the polytopic-type uncertain discrete-time switched system with MPDT are first designed. Finally, the effectiveness and potential of the proposed approaches is demonstrated by a water-quality control system.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93B52 | Feedback control |
| 93D09 | Robust stability |
| 93D20 | Asymptotic stability in control theory |
| 93C41 | Control/observation systems with incomplete information |
| 93C55 | Discrete-time control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
Keywords:
robust \(\mathcal{H}_\infty\) static output feedback control; uncertain discrete-time switched systems; robust global uniform asymptotic stabilityReferences:
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