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Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control

Author

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  • M. V. Thuan

    (Thai Nguyen University)

  • V. N. Phat

    (VAST)

Abstract

This paper deals with the problem of optimal guaranteed cost control for linear systems with interval time-varying delayed state and control. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. A linear–quadratic cost function is considered as a performance measure for the closed-loop system. By constructing a set of augmented Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a guaranteed cost controller design is presented and sufficient conditions for the existence of a guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9920-5
    DOI: 10.1007/s10957-011-9920-5
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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. 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. J. H. Park, 2005. "Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 491-502, February.
    4. Li, Huaizhong & Niculescu, Silviu-Iulian & Dugard, Luc & Dion, Jean-Michel, 1998. "Robust guaranteed cost control of uncertain linear time-delay systems using dynamic output feedback," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(3), pages 349-358.
    5. O. M. Kwon & J. H. Park & S. M. Lee, 2008. "Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 521-532, June.
    6. Z. Q. Zuo & Y. J. Wang, 2008. "Novel Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 159-170, October.
    7. Yang, Dedong & Cai, Kai-Yuan, 2010. "Reliable guaranteed cost sampling control for nonlinear time-delay systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2005-2018.
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    Cited by:

    1. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).

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