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

Author

Listed:
  • Xinghua Liu
  • Hongsheng Xi

Abstract

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.

Suggested Citation

  • Xinghua Liu & Hongsheng Xi, 2013. "On Delay‐Range‐Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:101485
    DOI: 10.1155/2013/101485
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    References listed on IDEAS

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    1. Qian-hong Zhang & Li-hui Yang, 2012. "Dynamical analysis of fuzzy BAM neural networks with variable delays," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 93-104, March.
    2. Qian-hong Zhang & Li-hui Yang, 2012. "Dynamical Analysis of Fuzzy BAM Neural Networks with Variable Delays," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 4(1), pages 93-104, March.
    3. Qianhong Zhang & Lihui Yang & Jingzhong Liu, 2012. "Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Karimi, Hamid Reza & Zapateiro, Mauricio & Luo, Ningsu, 2009. "Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 595-603.
    5. Qianhong Zhang & Lihui Yang & Jingzhong Liu, 2012. "Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, February.
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