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

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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.

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Acknowledgements

The authors would like to thank the reviewers and the editor for their very helpful comments and suggestions, which have improved our paper. This work is supported by the National Foundation for Science and Technology Development, Vietnam under grant 101.01.2011.51 and the Australian Research Council under the Discovery grant DP0667181.

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Authors and Affiliations

  1. Department of Mathematics, Quynhon University, Binhdinh, Vietnam

    P. T. Nam

  2. School of Engineering, Deakin University, Geelong, VIC, 3217, Australia

    P. N. Pathirana & H. Trinh

Authors
  1. P. T. Nam
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  2. P. N. Pathirana
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  3. H. Trinh
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Correspondence to P. T. Nam.

Additional information

Communicated by Martin Corless.

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Nam, P.T., Pathirana, P.N. & Trinh, H. Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances. J Optim Theory Appl 157, 843–852 (2013). https://doi.org/10.1007/s10957-012-0240-1

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  • DOI: https://doi.org/10.1007/s10957-012-0240-1

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