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Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays

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  • Xia Zhou
  • Shouming Zhong

Abstract

The mean square BIBO stabilization is investigated for the stochastic control systems with time delays and nonlinear perturbations. A class of suitable Lyapunov functional is constructed, combined with the descriptor model transformation and the decomposition technique of coefficient matrix; thus some novel delay‐dependent mean square BIBO stabilization conditions are derived. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Finally, three numerical examples are given to demonstrate that the derived conditions are effective and much less conservative than those given in the literature.

Suggested Citation

  • Xia Zhou & Shouming Zhong, 2013. "Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:586095
    DOI: 10.1155/2013/586095
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    References listed on IDEAS

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    1. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian‐Jumping Cohen‐Grossberg Neural Networks with Nonlinear p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Wang, Zidong & Shu, Huisheng & Liu, Yurong & Ho, Daniel W.C. & Liu, Xiaohui, 2006. "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 886-896.
    3. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear -Laplace Diffusion," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-21, May.
    4. Jincheng Wei & Peng Shi & Hamid Reza Karimi & Bo Wang, 2013. "BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    5. Jincheng Wei & Peng Shi & Hamid Reza Karimi & Bo Wang, 2013. "BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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