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Reachable set bounding for linear systems with mixed delays and state constraints

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  • Chen, Ruihan
  • Guo, Moxuan
  • Zhu, Song
  • Qi, Yongqiang
  • Wang, Min
  • Hu, Junhao

Abstract

This paper studies the reachable set estimation for systems with mixed delays and state constraints. Firstly, by constructing an appropriate maximal Lyapunov–Krasovskii functional, combined with the wirtinger-based integral inequality and the extended reciprocally convex combination method, we derive a new criterion about reachable set estimation which reduces the related decision variables without increasing the computational burden. Then, the results are extended to polytopic uncertainties systems and we consider the condition of uncertain differentiable parameters. Three examples are presented to demonstrate the validity of our theorems.

Suggested Citation

  • Chen, Ruihan & Guo, Moxuan & Zhu, Song & Qi, Yongqiang & Wang, Min & Hu, Junhao, 2022. "Reachable set bounding for linear systems with mixed delays and state constraints," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001692
    DOI: 10.1016/j.amc.2022.127085
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    References listed on IDEAS

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    1. 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).
    2. Liu, Guobao & Xu, Shengyuan & Wei, Yunliang & Qi, Zhidong & Zhang, Zhengqiang, 2018. "New insight into reachable set estimation for uncertain singular time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 769-780.
    3. Zhang, Liang & Feng, Zhiguang & Jiang, Zhengyi & Zhao, Ning & Yang, Yang, 2020. "Improved results on reachable set estimation of singular systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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    Cited by:

    1. Feng, Zhiguang & Zhang, Xinyue & Lam, James & Fan, Chenchen, 2023. "Estimation of reachable set for switched singular systems with time-varying delay and state jump," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    2. Liao, Wei & Liang, Taotao & Wang, Chen & Yang, Dayong, 2023. "A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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