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

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  • Xinghua Liu
  • Hongsheng Xi

Abstract

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.

Suggested Citation

  • Xinghua Liu & Hongsheng Xi, 2013. "On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode‐Dependent Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:691650
    DOI: 10.1155/2013/691650
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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. Shen, Chang-Chun & Zhong, Shou-Ming, 2009. "New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2277-2285.
    3. 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.
    4. 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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