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Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

Author

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  • Nguyen D. That

    (University of Technology)

  • Phan T. Nam

    (Quynhon University)

  • Q. P. Ha

    (University of Technology)

Abstract

This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. A numerical example is given to illustrate the effectiveness of the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0179-2
    DOI: 10.1007/s10957-012-0179-2
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    References listed on IDEAS

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    1. V. N. Phat & P. Niamsup, 2006. "Stabilization of Linear Nonautonomous Systems with Norm-Bounded Controls," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 135-149, October.
    2. C. Durieu & É. Walter & B. Polyak, 2001. "Multi-Input Multi-Output Ellipsoidal State Bounding," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 273-303, November.
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    Citations

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    Cited by:

    1. 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.
    2. Chang-Hua Lien & Hao-Chin Chang & Ker-Wei Yu & Hung-Chi Li & Yi-You Hou, 2021. "Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    3. Yuangong Sun & Fanwei Meng, 2017. "Reachable Set Estimation for a Class of Nonlinear Time-Varying Systems," Complexity, Hindawi, vol. 2017, pages 1-6, July.
    4. Xingao Zhu & Yuangong Sun, 2019. "Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance," Complexity, Hindawi, vol. 2019, pages 1-6, July.
    5. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    6. 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.
    7. Yucai Ding & Hui Liu, 2018. "Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems," Complexity, Hindawi, vol. 2018, pages 1-10, June.
    8. Chengdan Wang & Hongli Yang & Ivan Ganchev Ivanov, 2023. "Controlled Invariant Sets of Discrete-Time Linear Systems with Bounded Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-16, August.

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