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Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time

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  • Zhai, Ding
  • Lu, An-Yang
  • Li, Jing-Hao
  • Zhang, Qing-Ling

Abstract

This paper investigates the problem of the simultaneous fault detection and control (SFDC) for switched linear systems. To meet the control and detection objectives, the time-dependent detection filters and dynamic output feedback controllers are presented in SFDC under a mixed H∞/H− framework. A mode-dependent average dwell-time (MDADT) approach, which means that each subsystem has its own average dwell time, is adopted in this paper to reduce the conservativeness of the average dwell time method. And the discretized Lyapunov function (DLF) technique is first used to relax the MDADT constraints in SFDC. Some sufficient conditions for designing filters/controllers which satisfy the H∞/H− performance are given in terms of linear matrix inequalities (LMIs). What’s more, a two-step algorithm to solve the SFDC problem is proposed. The effectiveness of the proposed method is illustrated through two simulation examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:767-792
    DOI: 10.1016/j.amc.2015.10.062
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    1. Melania M. Moldovan & M. Seetharama Gowda, 2010. "On Common Linear/Quadratic Lyapunov Functions for Switched Linear Systems," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias & Akhtar A. Khan (ed.), Nonlinear Analysis and Variational Problems, chapter 0, pages 415-429, Springer.
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    Cited by:

    1. Göksu, Gökhan & Başer, Ulviye, 2021. "Finite-time stability for switched linear systems by Jordan decomposition," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Liu, Yanli & Wang, Runzhi & Hao, Li-Ying, 2022. "Adaptive TD control of full-state-constrained nonlinear stochastic switched systems," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2017. "Stability analysis and state feedback control of continuous-time T–S fuzzy systems via anew switched fuzzy Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 586-599.
    4. Liu, Xuan & Zhai, Ding & He, Da-Kuo & Chang, Xiao-Heng, 2018. "Simultaneous fault detection and control for continuous-time Markovian jump systems with partially unknown transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 469-486.
    5. Gao, Rui & Zhai, Ding & Cheng, Jun, 2019. "Decentralized static output feedback sliding mode control for interconnected descriptor systems via linear sliding variable," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 185-198.
    6. Wang, Qingzhi & He, Yong & Tan, Guanzheng & Wu, Min, 2017. "Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 438-447.
    7. Meng, Xin & Zhai, Ding & Fu, Zhumu & Xie, Xiangpeng, 2020. "Adaptive fault tolerant control for a class of switched nonlinear systems with unknown control directions," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. Zhao, Xiao-Qi & Guo, Shun & Long, Yue & Zhong, Guang-Xin, 2022. "Simultaneous fault detection and control for discrete-time switched systems under relaxed persistent dwell time switching," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    9. Xiong, Jun & Chang, Xiao-Heng & Yi, Xiaojian, 2018. "Design of robust nonfragile fault detection filter for uncertain dynamic systems with quantization," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 774-788.
    10. Pan, Yingnan & Yang, Guang-Hong, 2019. "Event-based output tracking control for fuzzy networked control systems with network-induced delays," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 513-530.
    11. Gao, Lijun & Wang, Zhenyue & Sun, Tao & Cao, Zhengbao, 2023. "Stability analysis for hybrid deterministic system under delay-dependent impulses uniting properties of edges," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    12. 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.
    13. Li, Jian & Wu, Chun-Yu, 2017. "Finite-time fault detection filter design for discrete-time interconnected systems with average dwell time," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 259-270.
    14. Du, Dongsheng, 2017. "Fault detection for discrete-time linear systems based on descriptor observer approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 575-585.
    15. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.

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