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Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances

Author

Listed:
  • P. T. Nam

    (Quynhon University)

  • P. N. Pathirana

    (Deakin University)

  • H. Trinh

    (Deakin University)

Abstract

In this paper, the problem of control design for exponential convergence of state/input delay systems with bounded disturbances is considered. Based on the Lyapunov–Krasovskii method combining with the delay-decomposition technique, a new sufficient condition is proposed for the existence of a state feedback controller, which guarantees that all solutions of the closed-loop system converge exponentially (with a pre-specified convergence rate) within a ball whose radius is minimized. The obtained condition is given in terms of matrix inequalities with one parameter needing to be tuned, which can be solved by using a one-dimensional search method with Matlab’s LMI Toolbox to minimize the radius of the ball. Two numerical examples are given to illustrate the superiority of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0240-1
    DOI: 10.1007/s10957-012-0240-1
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    References listed on IDEAS

    as
    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. 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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    Cited by:

    1. Yuangong Sun & Fanwei Meng, 2017. "Reachable Set Estimation for a Class of Nonlinear Time-Varying Systems," Complexity, Hindawi, vol. 2017, pages 1-6, July.
    2. Xingao Zhu & Yuangong Sun, 2019. "Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance," Complexity, Hindawi, vol. 2019, pages 1-6, July.

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