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A new method of reachable sets estimation for the nonlinear switched singular system with impulsive performance and time-delay

Author

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  • Feng, Zhiguang
  • Zhang, Xinyue
  • Liu, Jason J.R.
  • Jiang, Zhengyi

Abstract

This paper addresses the reachable set problem on nonlinear switched singular systems with impulsive performance and time-delay under bounded disturbance. The goal is to provide a real-time bounding set containing all reachable states. Originally, a real-time bounding criterion is developed by analyzing the variation of subinterval piecewise function and combining the definition of the average impulsive interval. Additionally, a lower bound on the Lyapunov function is provided by introducing an inequality scaling technique to avoid acquiring state bounds based on system decomposition techniques. Subsequently, the real-time bounding closed set, including all reachable states of the system, is estimated by calculating the Dini derivative of the Lyapunov function and using the real-time bounding criterion and the integral inequality technique. Finally, several numerical examples are given to illustrate the validity of the results obtained in this study.

Suggested Citation

  • Feng, Zhiguang & Zhang, Xinyue & Liu, Jason J.R. & Jiang, Zhengyi, 2024. "A new method of reachable sets estimation for the nonlinear switched singular system with impulsive performance and time-delay," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324003904
    DOI: 10.1016/j.amc.2024.128929
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    References listed on IDEAS

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    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. 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).
    3. Peixoto, Márcia L.C. & Coutinho, Pedro H.S. & Nguyen, Anh-Tu & Guerra, Thierry-Marie & Palhares, Reinaldo M., 2024. "Fault estimation for nonlinear parameter-varying time-delayed systems," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    4. Tu, Kairong & Xue, Yu & Zhang, Xian, 2024. "A new approach based on system solutions for passivity analysis of discrete-time memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 469(C).
    5. Shen, Zhihao & Zhang, Liang & Niu, Ben & Zhao, Ning, 2023. "Event-based reachable set synthesis for delayed nonlinear semi-Markov systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Yang, Anqing & Ma, Shuping, 2023. "Event-triggered control for switched singular systems with asynchronous switching and state jumps," Applied Mathematics and Computation, Elsevier, vol. 437(C).
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