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An Improved Delay-Dependent Criterion for Asymptotic Stability of Uncertain Dynamic Systems with Time-Varying Delays

Author

Listed:
  • O. M. Kwon

    (Chungbuk National University)

  • J. H. Park

    (Yeungnam University)

  • S. M. Lee

    (Daegu University)

Abstract

In this paper, the problem of stability analysis for uncertain dynamic systems with time-varying delays is considered. The parametric uncertainties are assumed to be bounded in magnitude. Based on the Lyapunov stability theory, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities, which can be solved easily by various efficient convex optimization algorithms. Two numerical examples are illustrated to show the effectiveness of proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9637-x
    DOI: 10.1007/s10957-009-9637-x
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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. 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.
    3. 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.
    4. 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.
    5. C. H. Lien, 2005. "H∞ Observer-Based Control for a Class of Uncertain Neutral Time-Delay Systems via LMI Optimization Approach," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 129-144, October.
    6. 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.
    7. 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.
    8. J. D. Chen, 2009. "Delay-Dependent Nonfragile H ∞ Observer-Based Control for Neutral Systems with Time Delays in the State and Control Input," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 445-460, May.
    9. O. M. Kwon & J. H. Park, 2008. "Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 277-293, November.
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