Delay-dependent robust \(H_\infty\) control for uncertain stochastic time-delay systems. (English) Zbl 1203.93191

Yang, Rongni; Gao, Huijun; Shi, Peng

Int. J. Robust Nonlinear Control 20, No. 16, 1852-1865 (2010).

Summary: This paper investigates the robust \(H_\infty\) control problem for stochastic systems with a delay in the state. Sufficient delay-dependent conditions for the existence of state-feedback controllers are proposed to guarantee mean-square asymptotic stability as well as the prescribed \(H_\infty\) performance for closed-loop systems. Moreover, the results are further extended to the stochastic time-delay systems with parameter uncertainties, which are assumed to be time-varying norm-bounded appearing in both the state and the input matrices. The appealing idea is to split the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques.

MSC:

93E03	Stochastic systems in control theory (general)
93B36	\(H^\infty\)-control
93E15	Stochastic stability in control theory
93D20	Asymptotic stability in control theory

Keywords:

stochastic systems; time delay; uncertainties; \(H_\infty\) control; delay partitioning; Lyapunov-Krasovskii functional

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