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\(H_\infty\) finite time control for discrete time-varying system with interval time-varying delay. (English) Zbl 1395.93343

Summary: This paper discusses the problem of \(H_\infty\) finite time control for a discrete time-varying system with interval time-varying delay. By constructing a new augmented time-varying Lyapunov functional involving triple summation items and using discrete Wirtinger-type inequalities, delay-dependent conditions are derived, which guarantee that the closed-loop system is not only finite time bounded (FTB) but also satisfies an \(H_\infty\) performance. Furthermore, the time-varying feedback controller can be derived by solving a series of recursive linear matrix inequalities (RLMIs). Simulation results show the effectiveness and superiority of the proposed method.

MSC:

93C55 Discrete-time control/observation systems
93B36 \(H^\infty\)-control
93C05 Linear systems in control theory
93D15 Stabilization of systems by feedback
93D30 Lyapunov and storage functions
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