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Finite-time dissipative control for discrete-time stochastic delayed systems with Markovian switching and interval parameters. (English) Zbl 1490.93112

Summary: The problem of finite-time dissipative control for discrete-time stochastic delayed systems (DTSDSs) with Markovian switching and interval parameters is studied in this paper. Firstly, DTSDSs are equivalently transformed into discrete-time uncertain stochastic delayed systems, whose interval parameters are described by a series of convex combinations of the endpoints information. Then, finite-time stochastic boundedness (FTSB) and finite-time stochastic exponential \((Q_i,S_i,R_i)-\alpha\) dissipative (FTSED) are analysed by constructing a discrete-time Lyapunov-Krasovskii functional. Correspondingly, several sufficient conditions are obtained in terms of linear matrix inequalities (LMIs). Furthermore, the delay-feedback controllers with memory are designed such that the finite-time dissipative performance of the DTSDSs is satisfied. Finally, the proposed results are validated through a switching energy-storing electrical circuit.

MSC:

93D40 Finite-time stability
93C55 Discrete-time control/observation systems
93E15 Stochastic stability in control theory
93C43 Delay control/observation systems
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