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Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays

Author

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  • T. Senthilkumar

    (Gandhigram Rural Institute-Deemed University)

  • P. Balasubramaniam

    (Gandhigram Rural Institute-Deemed University)

Abstract

This paper considers the problems of delay-dependent robust stabilization and H ∞ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays. Based on the Lyapunov method and introducing some appropriate free-weighting matrices, sufficient conditions for the solvability of above problems have been investigated in terms of linear matrix inequalities (LMIs). Furthermore, the desired state feedback controller has also been designed by solving these LMIs. Finally, a numerical example is provided to demonstrate the potential of the proposed techniques.

Suggested Citation

  • T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:1:d:10.1007_s10957-011-9858-7
    DOI: 10.1007/s10957-011-9858-7
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    References listed on IDEAS

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    1. P. T. Nam & V. N. Phat, 2009. "Robust Stabilization of Linear Systems with Delayed State and Control," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 287-299, February.
    2. Panos M. Pardalos & Vitaliy Yatsenko, 2008. "Control of Bilinear Systems," Springer Optimization and Its Applications, in: Optimization and Control of Bilinear Systems, chapter 0, pages 65-91, Springer.
    3. J. H. Park, 2001. "Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 155-174, January.
    4. O. Kwon & J. H. Park, 2005. "Matrix Inequality Approach to a Novel Stability Criterion for Time-Delay Systems with Nonlinear Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 643-656, September.
    5. Panos M. Pardalos & Vitaliy Yatsenko, 2008. "Optimization and Control of Bilinear Systems," Springer Optimization and Its Applications, Springer, number 978-0-387-73669-3, September.
    6. K. Benjelloun & E. K. Boukas & O. L. V. Costa, 2000. "H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 73-95, April.
    7. P. Shi & E. K. Boukas, 1997. "H ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 75-99, October.
    8. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

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