Finite-time \(H_\infty\) control for discrete-time Markov jump systems with actuator saturation. (English) Zbl 1461.93453

Li, Bo; Zhao, Junjie

Abstr. Appl. Anal. 2014, Article ID 182613, 7 p. (2014).

Summary: This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-time \(H_\infty\) controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

MSC:

93D40	Finite-time stability
93B36	\(H^\infty\)-control
93E15	Stochastic stability in control theory
93D20	Asymptotic stability in control theory
93C55	Discrete-time control/observation systems

Keywords:

finite-time \(H_\infty\) control; discrete-time Markov jump systems; asymptotic stabilization

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