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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. 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.
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    8. 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.
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    Cited by:

    1. Xie, Jing & Kao, Yonggui & Wang, Changhong & Gao, Cunchen, 2015. "Delay-dependent robust stability of uncertain neutral-type Itoˆ stochastic systems with Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 576-585.
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    3. Wang, Guoliang & Zhang, Qingling & Yang, Chunyu & Su, Chengli, 2015. "Stabilization of continuous-time randomly switched systems via the LMI approach," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 527-538.
    4. Zhou, Yaoyao & Chen, Gang, 2021. "Non-fragile H∞ finite-time sliding mode control for stochastic Markovian jump systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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