Robust \(H_\infty\) control for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities
type: Item
instance of: scholarly article
title: Robust \(H_\infty\) control for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities
zbMATH Open document ID: 1406.93110
DOI: 10.1155/2014/170794
author: Yamin Wang
author: Stanislao Lauria
author: Yurong Liu
author: Fuad E. Alsaadi
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 93E03
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93D09
zbMATH DE Number: 7021857
zbMATH Keywords: robust \(H_\infty\) control
zbMATH Keywords: discrete time-delay stochastic systems
zbMATH Keywords: state feedback controller
zbMATH Keywords: robust asymptotic stability
Wikidata QID: Q59035708
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/170794
OpenAlex ID: W2127234541
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description: scientific article; zbMATH DE number 7021857