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Global exponential stability and H∞ control of limit cycle for switched affine systems under time-dependent switching signal

Author

Listed:
  • Xu, Xiaozeng
  • Zhang, Hongbin
  • Zheng, Qunxian
  • Chen, Wei

Abstract

In this paper, the stability analysis of continuous-time switched affine systems (CTSASs) is addressed via dwell time switching. The main purpose of this note is to design a time-dependent switching signal assuring the global exponential stability of a desire limit cycle (which is selected from a set of attainable limit cycles). By constructing a discretized Lyapunov function and using the linear matrix inequalities technique, a set of conditions in the framework of dwell time are designed. For CTSASs, the performance indexes of the system in this neighborhood cannot be analyzed because most of the proposed controllers drive the system trajectory into a small enough neighborhood. Differently, the technique proposed in this note leads the CTSAS’s trajectory to the limit cycle so that the resulting conditions can consider the weighted H∞ performance level of the system. More specifically, the design conditions can be applied to open-loop subsystems that are unstable. At last, a numerical example and a practical example are given to illustrate our method.

Suggested Citation

  • Xu, Xiaozeng & Zhang, Hongbin & Zheng, Qunxian & Chen, Wei, 2022. "Global exponential stability and H∞ control of limit cycle for switched affine systems under time-dependent switching signal," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300321008894
    DOI: 10.1016/j.amc.2021.126807
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    References listed on IDEAS

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    1. Xiao Han & Zhijian Ji & Qingyuan Qi, 2020. "Optimal Control for Networked Control Systems with Markovian Packet Losses," Complexity, Hindawi, vol. 2020, pages 1-11, November.
    2. Xing, Mengping & Xia, Jianwei & Wang, Jing & Meng, Bo & Shen, Hao, 2019. "Asynchronous H∞ filtering for nonlinear persistent dwell-time switched singular systems with measurement quantization," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Li, Jiahao & Liu, Yu & Yu, Jinyong & Sun, Yiming & Liu, Mengmeng, 2021. "A new result of terminal sliding mode finite-time state and fault estimation for a class of descriptor switched systems," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. 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.
    5. Li, Zhi-Min & Chang, Xiao-Heng & Yu, Lu, 2016. "Robust quantized H∞ filtering for discrete-time uncertain systems with packet dropouts," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 361-371.
    6. Dany Ivan Martinez & José de Jesús Rubio & Arturo Aguilar & Jaime Pacheco & Guadalupe Juliana Gutierrez & Victor Garcia & Tomas Miguel Vargas & Genaro Ochoa & David Ricardo Cruz & Cesar Felipe Juarez, 2020. "Stabilization of Two Electricity Generators," Complexity, Hindawi, vol. 2020, pages 1-13, December.
    7. Song, Jia-Sheng & Chang, Xiao-Heng, 2020. "H∞ controller design of networked control systems with a new quantization structure," Applied Mathematics and Computation, Elsevier, vol. 376(C).
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