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Mixed H∞ and passive control for linear switched systems via hybrid control approach

Author

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  • Qunxian Zheng
  • Youzhu Ling
  • Lisheng Wei
  • Hongbin Zhang

Abstract

This paper investigates the mixed H∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.

Suggested Citation

  • Qunxian Zheng & Youzhu Ling & Lisheng Wei & Hongbin Zhang, 2018. "Mixed H∞ and passive control for linear switched systems via hybrid control approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 818-832, March.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:4:p:818-832
    DOI: 10.1080/00207721.2018.1424967
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    Cited by:

    1. Harshavarthini, S. & Sakthivel, R. & Kong, F., 2020. "Finite-time synchronization of chaotic coronary artery system with input time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Vijayakumar, M. & Sakthivel, R. & Mohammadzadeh, Ardashir & Karthick, S.A. & Marshal Anthoni, S., 2021. "Proportional integral observer based tracking control design for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    4. Abinandhitha, R. & Sakthivel, R. & Tatar, N. & Manikandan, R., 2022. "Anti-disturbance observer-based control for fuzzy chaotic semi-Markov jump systems with multiple disturbances and mixed actuator failures," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Houssem Jerbi & Mourad Kchaou & Attia Boudjemline & Mohamed Amin Regaieg & Sondes Ben Aoun & Ahmed Lakhdar Kouzou, 2021. "H ∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults," Mathematics, MDPI, vol. 9(18), pages 1-25, September.

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