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Finite-time stabilization of switched nonlinear systems with partial unstable modes

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  • Wang, Yijing
  • Zou, Yanchao
  • Zuo, Zhiqiang
  • Li, Hongchao

Abstract

This paper investigates the finite-time stabilization problem of switched nonlinear systems (SNS) in the presence of impulse effects, where both stable subsystems and unstable subsystems coexist. A new notion named mode-dependent average switching frequency (MDASF) is firstly proposed by extending the previous average switching frequency method (ASF). Designing mode-dependent switching law reveals the tradeoff among stable and unstable modes. Based on the estimation on transition matrix and Gronwall–Bellman inequality, mode-dependent feedback controllers are constructed to achieve finite-time stability of the closed-loop systems. Finally, a numerical example is given to verify the efficiency of the proposed method and the validity of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:172-181
    DOI: 10.1016/j.amc.2016.06.015
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    References listed on IDEAS

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    1. Gao, Lijun & Wang, Dandan & Wang, Gang, 2015. "Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 186-200.
    2. Lin, Xiangze & Li, Xueling & Li, Shihua & Zou, Yun, 2016. "Finite-time boundedness for switched systems with sector bounded nonlinearity and constant time delay," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 25-40.
    3. Zhao, Ping & Feng, Wei & Zhao, Yan & Kang, Yu, 2015. "Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1038-1054.
    4. Yu, Qiang & Zhao, Xudong, 2016. "Stability analysis of discrete-time switched linear systems with unstable subsystems," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 718-725.
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    Cited by:

    1. Zhu, Hao-Yang & Jiang, Xiaoyue & Li, Yuan-Xin & Tong, Shaocheng, 2023. "Finite-time adaptive fuzzy output tracking of switched nonlinear systems with ISD-ADT," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. 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.
    3. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    4. Wang, Zhe & Xue, Dingyu & Pan, Feng, 2021. "Observer-based robust control for singular switched fractional order systems subject to actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    5. Ding, Kui & Zhu, Quanxin, 2019. "H∞ synchronization of uncertain stochastic time-varying delay systems with exogenous disturbance via intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 244-256.
    6. Lin, Xiangze & Li, Shihua & Zou, Yun, 2017. "Finite-time stabilization of switched linear time-delay systems with saturating actuators," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 66-79.
    7. 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.
    8. Fu, Teng & Zhou, Yusheng, 2022. "Stabilization of switched time-delay systems with only unstable subsystems: a new approach based on a vibration model of 1.5 degrees of freedom," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    9. 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.

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