Stability Analysis for Neutral Delay Markovian Jump Systems with Nonlinear Perturbations and Partially Unknown Transition Rates | Zendy

Xinghua Liu | Zendy; Hongsheng Xi | Zendy

Open Access

Stability Analysis for Neutral Delay Markovian Jump Systems with Nonlinear Perturbations and Partially Unknown Transition Rates

Author(s) -

Xinghua Liu,

Hongsheng Xi

Publication year - 2013

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2013/592483

Subject(s) - mathematics , nonlinear system , exponential stability , lemma (botany) , weighting , control theory (sociology) , upper and lower bounds , stability (learning theory) , transition rate matrix , jump , interval (graph theory) , convex combination , range (aeronautics) , convex optimization , regular polygon , mathematical analysis , computer science , physics , statistics , combinatorics , materials science , artificial intelligence , ecology , acoustics , composite material , biology , geometry , control (management) , quantum mechanics , machine learning , poaceae

The problem of exponential stability for the uncertain neutral Markovian jump systems with interval time-varying delays and nonlinear perturbations is investigated in this paper. This study starts from the corresponding nominal systems with known and partially unknown transition rates, respectively. By constructing a novel augmented Lyapunov functional which contains triple-integral terms and fully utilizes the bound of the delay, the delay-range-dependent and rate-dependent exponential stability criteria are developed by the Lyapunov theory, reciprocally convex lemma, and free weighting matrices. Then, the results about nominal systems are extended to the uncertain case. Finally, numerical examples are given to demonstrate the effectiveness of the proposed methods

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