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Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

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  • Lianglin Xiong
  • Xiaobing Zhou
  • Jie Qiu
  • Jing Lei

Abstract

The delay‐dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov‐Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:450168
    DOI: 10.1155/2012/450168
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    References listed on IDEAS

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    1. Balasubramaniam, P. & Lakshmanan, S. & Manivannan, A., 2012. "Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 483-495.
    2. Guan, Zhi-Hong & Zhang, Hao, 2008. "Stabilization of complex network with hybrid impulsive and switching control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1372-1382.
    3. Xiong, Lianglin & Zhong, Shouming & Ye, Mao & Wu, Shiliang, 2009. "New stability and stabilization for switched neutral control systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1800-1811.
    4. Liu, Xinzhi & Teo, Kok-Lay & Zhang, Hongtao & Chen, Guanrong, 2006. "Switching control of linear systems for generating chaos," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 725-733.
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    Cited by:

    1. 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).
    2. 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).

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