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Robust Stabilization of Linear Systems with Delayed State and Control

Author

Listed:
  • P. T. Nam

    (Qui Nhon University)

  • V. N. Phat

    (Institute of Mathematics)

Abstract

Robust stabilization of linear systems with delays on both the state and control input is studied in this paper. Using an improved Lyapunov-Krasovskii functional, we establish new criteria that ensure the robust stability of the closed-loop system with memoryless state feedback controls. The generalized conditions are derived in terms of linear matrix inequalities (LMIs), allowing us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution and can be easily solved by numerical algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:2:d:10.1007_s10957-008-9453-8
    DOI: 10.1007/s10957-008-9453-8
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    References listed on IDEAS

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    1. V. N. Phat & P. Niamsup, 2006. "Stabilization of Linear Nonautonomous Systems with Norm-Bounded Controls," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 135-149, October.
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    Cited by:

    1. P. T. Nam & P. N. Pathirana & H. Trinh, 2013. "Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 843-852, June.
    2. V. N. Phat & Q. P. Ha & H. Trinh, 2010. "Parameter-dependent H ∞ Control for Time-varying Delay Polytopic Systems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 58-70, October.
    3. K. Ramakrishnan & G. Ray, 2011. "Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 366-384, May.
    4. M. V. Thuan & V. N. Phat, 2012. "Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 394-412, February.
    5. O. M. Kwon & J. H. Park & S. M. Lee, 2010. "An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 343-353, May.
    6. 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.
    7. Chun Yin & Shouming Zhong & Xiaoyun Liu & Zijian Liu, 2011. "Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 81-99, October.

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    1. V. N. Phat & Q. P. Ha, 2009. "H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 603-618, September.
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