中国物理B ›› 2023, Vol. 32 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/acedf5

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Finite-time H∞ filtering for Markov jump systems with uniform quantization

Jingjing Dong(董敬敬)1, Xiaofeng Ma(马晓峰)1, Xiaoqing Zhang(张晓庆)1, Jianping Zhou(周建平)1,†, and Zhen Wang(王震)2   

  1. 1 School of Computer Science & Technology, Anhui University of Technology, Ma'anshan 243032, China;
    2 College of Mathematics & Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
  • 收稿日期:2023-05-31 修回日期:2023-07-24 接受日期:2023-08-08 出版日期:2023-10-16 发布日期:2023-11-07
  • 通讯作者: Jianping Zhou E-mail:jpzhou0@gmail.com
  • 基金资助:
    Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2020A0248 and 2022AH050310).

Finite-time H∞ filtering for Markov jump systems with uniform quantization

Jingjing Dong(董敬敬)1, Xiaofeng Ma(马晓峰)1, Xiaoqing Zhang(张晓庆)1, Jianping Zhou(周建平)1,†, and Zhen Wang(王震)2   

  1. 1 School of Computer Science & Technology, Anhui University of Technology, Ma'anshan 243032, China;
    2 College of Mathematics & Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
  • Received:2023-05-31 Revised:2023-07-24 Accepted:2023-08-08 Online:2023-10-16 Published:2023-11-07
  • Contact: Jianping Zhou E-mail:jpzhou0@gmail.com
  • Supported by:
    Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Grant Nos. KJ2020A0248 and 2022AH050310).

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摘要： This paper is concerned with finite-time H∞ filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H∞ performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur's complement, and Dynkin's formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.

关键词: Markov jump system, filter design, finite-time H∞ performance, uniform quantization

Abstract: This paper is concerned with finite-time H∞ filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time H∞ performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur's complement, and Dynkin's formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.

Key words: Markov jump system, filter design, finite-time H∞ performance, uniform quantization

中图分类号:  (Control theory)

  • 02.30.Yy
02.50.Ga (Markov processes) 87.19.lr (Control theory and feedback)