New Stochastic Stability Criteria for Nonlinear Neutral Markovian Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

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

Abstract and Applied Analysis ◽

10.1155/2013/691650 ◽

2013 ◽

Vol 2013 ◽

pp. 1-23

Author(s):

Xinghua Liu ◽

Hongsheng Xi

Keyword(s):

Exponential Stability ◽

Lyapunov Stability Theory ◽

Markovian Jump Systems ◽

Time Varying ◽

Transition Rates ◽

Stability Criteria ◽

Markovian Jump ◽

Rate Dependent ◽

Partially Known Transition Rates ◽

Jump Systems

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.

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On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems

Journal of Applied Mathematics ◽

10.1155/2013/101485 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Xinghua Liu ◽

Hongsheng Xi

Keyword(s):

Stochastic Stability ◽

Convex Combination ◽

Markovian Jump Systems ◽

Linear Matrix ◽

Stability Conditions ◽

Time Varying ◽

Matrix Inequalities ◽

Markovian Jump ◽

Neutral Delay ◽

Jump Systems

The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov functional which contains some triple-integral terms is introduced. Then, by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability conditions are presented in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

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