On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays

On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays

The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique...

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Main Authors: Xinghua Liu, Hongsheng Xi
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/691650
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spelling doaj-5e394ec4bcef4a5fb1a3f3b234e1f2952020-11-24T21:04:04ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/691650691650On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent DelaysXinghua Liu0Hongsheng Xi1Department of Auto, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaDepartment of Auto, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, ChinaThe exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.http://dx.doi.org/10.1155/2013/691650
collection DOAJ
language English
format Article
sources DOAJ
author Xinghua Liu
Hongsheng Xi
spellingShingle Xinghua Liu
Hongsheng Xi
On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
Abstract and Applied Analysis
author_facet Xinghua Liu
Hongsheng Xi
author_sort Xinghua Liu
title On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
title_short On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
title_full On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
title_fullStr On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
title_full_unstemmed On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
title_sort on exponential stability for a class of uncertain neutral markovian jump systems with mode-dependent delays
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.
url http://dx.doi.org/10.1155/2013/691650
work_keys_str_mv AT xinghualiu onexponentialstabilityforaclassofuncertainneutralmarkovianjumpsystemswithmodedependentdelays
AT hongshengxi onexponentialstabilityforaclassofuncertainneutralmarkovianjumpsystemswithmodedependentdelays
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