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Exponential Stability for Uncertain Dynamic Systems with Time-Varying Delays: LMI Optimization Approach

Author

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  • O. M. Kwon

    (Chungbuk National University)

  • J. H. Park

    (Yeungnam University)

  • S. M. Lee

    (BcN Business Unit, KT CO. Ltd.)

Abstract

In this paper, we consider dynamic systems with uncertainties and time-varying delays. Based on the Lyapunov method and convex optimization approach, a delay-dependent criterion for exponential stability of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, an interior-point algorithm is utilized in this work. Numerical examples are illustrated to show the effectiveness of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-008-9357-7
    DOI: 10.1007/s10957-008-9357-7
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    References listed on IDEAS

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    1. Park, Ju H. & Choi, K., 2005. "Guaranteed cost control of uncertain nonlinear neutral systems via memory state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 183-190.
    2. J. H. Park, 2005. "Convex Optimization Approach to Dynamic Output Feedback Control for Delay Differential Systems of Neutral Type," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 411-423, November.
    3. J. H. Park & S. Won, 1999. "Asymptotic Stability of Neutral Systems with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 183-200, October.
    4. J. H. Park, 2004. "On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 147-162, April.
    5. M. S. Mahmoud & M. Zribi, 1999. "H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 89-122, January.
    6. C. H. Lien, 2005. "Guaranteed Cost Observer–Based Controls for a Class of Uncertain Neutral Time-Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 137-156, July.
    7. 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.
    8. C.H. Lien, 2005. "Stability and Stabilization Criteria for a Class of Uncertain Neutral Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 637-657, March.
    9. O. M. Kown & J. H. Park, 2006. "Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 391-414, June.
    10. 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.
    11. O. M. Kwon & J. H. Park & S. M. Lee & S. C. Won, 2006. "LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 103-117, January.
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    Cited by:

    1. Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    2. 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.

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