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Incremental H∞ control for switched nonlinear systems

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  • Ren, Yuanhong
  • Wang, Weiqun
  • Wang, Yixiang

Abstract

In this paper, we investigate the incremental H∞ control for switched nonlinear systems by using a state-dependent switching law and an average dwell time approach incorporated with multiple Lyapunov functions. Even if all subsystems are unstable, a sufficient condition for the incremental H∞ control problem to be solvable is derived based on the design state-dependent switching law. Furthermore, when all subsystems are incrementally globally asymptotically stable (IGAS), the switched nonlinear system under the average dwell time scheme is IGAS and possesses a weighted incremental L2-gain. Then, we extend this result to the case where both IGAS subsystems and unstable subsystems coexist, if the activation time ratio between IGAS subsystems and unstable ones is not less than a specified constant, sufficient conditions for the weighted incremental H∞ performance of the switched system are guaranteed. Two numerical examples are given to illustrate the validity of the proposed approach.

Suggested Citation

  • Ren, Yuanhong & Wang, Weiqun & Wang, Yixiang, 2018. "Incremental H∞ control for switched nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 251-263.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:251-263
    DOI: 10.1016/j.amc.2018.03.016
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    References listed on IDEAS

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    1. Cai, Chaohong & Chen, Guanrong, 2006. "Synchronization of complex dynamical networks by the incremental ISS approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 754-766.
    2. Ren, Hangli & Zong, Guangdeng & Hou, Linlin & Yi, Yang, 2016. "Finite-time control of interconnected impulsive switched systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 143-157.
    3. Changchun Hua & Guopin Liu & Zhenhua Bai & Xinping Guan, 2016. "Decentralised adaptive control for a class of stochastic switched interconnected nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(16), pages 3782-3791, December.
    4. Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
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    Cited by:

    1. Shi, Shuang & Fei, Zhongyang & Shi, Zhenpeng & Ren, Shunqing, 2018. "Stability and stabilization for discrete-time switched systems with asynchronism," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 520-536.
    2. 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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