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

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  • Xinghua Liu
  • Hongsheng Xi

Abstract

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.

Suggested Citation

  • Xinghua Liu & Hongsheng Xi, 2013. "Stability Analysis for Neutral Delay Markovian Jump Systems with Nonlinear Perturbations and Partially Unknown Transition Rates," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:592483
    DOI: 10.1155/2013/592483
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    References listed on IDEAS

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    1. Lianglin Xiong & Xiaobing Zhou & Jie Qiu & Jing Lei, 2012. "Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Zhang, Jinhui & Shi, Peng & Qiu, Jiqing, 2008. "Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 160-167.
    3. Lianglin Xiong & Xiaobing Zhou & Jie Qiu & Jing Lei, 2012. "Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-22, October.
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