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On backwards and forwards reachable sets bounding for perturbed time-delay systems

Author

Listed:
  • Trinh, H.
  • Nam, Phan T.
  • Pathirana, Pubudu N.
  • Le, H.P.

Abstract

Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov–Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.

Suggested Citation

  • Trinh, H. & Nam, Phan T. & Pathirana, Pubudu N. & Le, H.P., 2015. "On backwards and forwards reachable sets bounding for perturbed time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 664-673.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:664-673
    DOI: 10.1016/j.amc.2015.07.116
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    References listed on IDEAS

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    1. Nguyen D. That & Phan T. Nam & Q. P. Ha, 2013. "Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 96-107, April.
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    Cited by:

    1. Liao, Wei & Liang, Taotao & Wei, Xiaohui & Yin, Qiaozhi, 2022. "Probabilistic reach-Avoid problems in nondeterministic systems with time-Varying targets and obstacles," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Wei Kang & Hao Chen & Kaibo Shi & Jun Cheng, 2018. "Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs," Complexity, Hindawi, vol. 2018, pages 1-11, March.

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