Almost sure stability and stabilization for hybrid stochastic systems with time-varying delays
type: Item
instance of: scholarly article
title: Almost sure stability and stabilization for hybrid stochastic systems with time-varying delays
zbMATH Open document ID: 1264.93268
DOI: 10.1155/2012/183729
author: Hua Yang
author: Huisheng Shu
author: Xiu Kan
author: Yan Che
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: The problems of almost sure (a.s.) stability and a.s. stabilization are investigated for hybrid stochastic systems (HSSs) with time-varying delays. The different time-varying delays in the drift part and in the diffusion part are considered. Based on nonnegative semimartingale convergence theorem, Hölder's inequality, Doob's martingale inequality, and Chebyshev's inequality, some sufficient conditions are proposed to guarantee that the underlying nonlinear hybrid stochastic delay systems (HSDSs) are almost surely (a.s.) stable. With these conditions, a.s. stabilization problem for a class of nonlinear HSDSs is addressed through designing linear state feedback controllers, which are obtained in terms of the solutions to a set of linear matrix inequalities (LMIs). Two numerical simulation examples are given to show the usefulness of the results derived.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 34K50
zbMATH DE Number: 6173078
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/183729
OpenAlex ID: W2101047911
Wikidata QID: Q58912555
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description: scientific article; zbMATH DE number 6173078