## Abstract and Applied Analysis

### Robust ${H}_{\infty }$ Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

#### Abstract

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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 170794, 10 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425048760

Digital Object Identifier
doi:10.1155/2014/170794

Mathematical Reviews number (MathSciNet)
MR3259154

Zentralblatt MATH identifier
07021857

#### Citation

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. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 170794, 10 pages. doi:10.1155/2014/170794. https://projecteuclid.org/euclid.aaa/1425048760

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