华东师范大学学报(自然科学版) ›› 2020, Vol. 2020 ›› Issue (6): 16-23.doi: 10.3969/j.issn.1000-5641.201911036

• 数学 • 上一篇    下一篇

离散周期Markov跳变系统的鲁棒耗散控制

李秀英1, 姜囡2   

  1. 1. 通化师范学院 数学学院, 吉林 通化 134002;
    2. 中国刑事警察学院 声像资料检验技术系, 沈阳 110854
  • 收稿日期:2019-08-14 发布日期:2020-12-01
  • 作者简介:李秀英, 女, 教授, 研究方向为随机系统的控制. E-mail: xiuyingli68@163.com
  • 基金资助:
    国家自然科学基金青年基金(61304021)

Robust dissipative control for discrete-time periodic Markovian jump systems

LI Xiuying1, JIANG Nan2   

  1. 1. School of Mathematics, Tonghua Normal University, Tonghua Jilin 134002, China;
    2. Department of Audio-Visual and Image Technology, Criminal Investigation Police University of China, Shenyang 110854, China
  • Received:2019-08-14 Published:2020-12-01

摘要: 研究了一类具有不完全转移率的不确定离散周期Markov跳变系统的鲁棒耗散控制问题. 通过构造Lyapunov函数, 利用线性矩阵不等式, 设计周期状态反馈严格耗散控制器, 使闭环系统在转移率部分未知的条件下随机稳定且严格耗散. 最后, 通过数值算例验证了所提出方法的有效性.

关键词: 周期Markov跳变系统, 耗散控制, 不完全转移率, 线性矩阵不等式

Abstract: In this paper, we discuss the robust dissipative control problem of uncertain discrete-time periodic Markovian jump systems with incomplete transition rates. By employing the Lyapunov function, a periodic state feedback controller using linear matrix inequalities is designed, that ensures the resultant closed-loop system with incomplete transition rates is stochastically stable and strictly dissipative. Lastly, an example is given to illustrate the effectiveness of the proposed method.

Key words: periodic Markovian jump systems, dissipative control, incomplete transition rates, linear matrix inequality

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