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Stability and Stabilization of Nonlinear Switched Systems Under Average Dwell Time

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  • Liu, Lei
  • Zhou, Qi
  • Liang, Hongjing
  • Wang, Lijie

Abstract

In this paper, the problems of stability and stabilization of nonlinear discrete-time switched systems is investigated. Firstly, in order to implement the lower bound of minimum average dwell time (ADT) of discrete-time switched nonlinear systems, the ι -open-chain and quasi-cyclic switching signals are introduced. Secondly, the problem of these underlying nonlinear discrete-time switched systems are solved by using the interval type-2 (IT2) fuzzy modeling approach. Thirdly, a novel delayed IT2 fuzzy controller is devised to guarantee the asymptotically stable of the resulting systems. Finally, a numerical simulation example is given to show the merit and effectiveness of the proposed approach.

Suggested Citation

  • Liu, Lei & Zhou, Qi & Liang, Hongjing & Wang, Lijie, 2017. "Stability and Stabilization of Nonlinear Switched Systems Under Average Dwell Time," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 77-94.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:77-94
    DOI: 10.1016/j.amc.2016.11.006
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    References listed on IDEAS

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    1. Mahmoud, Magdi S. & Almutairi, Naif B., 2016. "Feedback fuzzy control for quantized networked systems with random delays," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 80-97.
    2. Wang, Yijing & Zou, Yanchao & Zuo, Zhiqiang & Li, Hongchao, 2016. "Finite-time stabilization of switched nonlinear systems with partial unstable modes," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 172-181.
    3. Zhai, Ding & Lu, An-Yang & Li, Jing-Hao & Zhang, Qing-Ling, 2016. "Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 767-792.
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    Cited by:

    1. Li, Yanan & Sun, Yuangong & Meng, Fanwei & Tian, Yazhou, 2018. "Exponential stabilization of switched time-varying systems with delays and disturbances," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 131-140.
    2. Zhou, Yusheng & Chen, Danhong, 2021. "Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. Xiao, Xiaoqing & Park, Ju H. & Zhou, Lei, 2018. "Event-triggered control of discrete-time switched linear systems with packet losses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 344-352.
    4. Cao, Zhengbao & Gao, Lijun & Wang, Gang, 2019. "Stability conditions of switched nonlinear systems with unstable subsystems and destabilizing switching behaviors," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    5. Wang, Zhichuang & Chen, Guoliang & Ba, Hezhen, 2019. "Stability analysis of nonlinear switched systems with sampled-data controllers," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 297-309.
    6. Göksu, Gökhan & Başer, Ulviye, 2021. "Finite-time stability for switched linear systems by Jordan decomposition," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    7. Zhu, Xingao & Liu, Shutang, 2022. "Reachable set estimation for continuous-time impulsive switched nonlinear time-varying systems with delay and disturbance," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    8. Yali Dong & Jing Hao & Yonghong Yao & Huimin Wang, 2019. "Robust Stabilization of Discrete-Time Switched Periodic Systems with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-13, February.

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