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Wang, Yamin; Alsaadi, Fuad E.; Lauria, Stanislao; Liu, Yurong

Robust \(H_\infty\) control for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. (English) Zbl 1406.93110

Abstr. Appl. Anal. 2014, Article ID 170794, 10 p. (2014).
Summary: In this paper, we consider the robust \(H_\infty\) control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribed \(H_\infty\) disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.

MSC:

93B36 \(H^\infty\)-control
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
93E03 Stochastic systems in control theory (general)
93B52 Feedback control
93D20 Asymptotic stability in control theory
93D09 Robust stability

Keywords:

robust \(H_\infty\) control; discrete time-delay stochastic systems; state feedback controller; robust asymptotic stability
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\textit{Y. Wang} et al., Abstr. Appl. Anal. 2014, Article ID 170794, 10 p. (2014; Zbl 1406.93110)
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References:

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