\(L_1\) Control for Positive Markovian Jump Systems with Time-Varying Delays and Partly Known Transition Rates

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• 作者：Wenhai Qi ; Xianwen Gao
• 关键词：Positive Markovian jump systems ; Partly known transition rates ; Stochastic stability ; Linear programming
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：34
• 期：8
• 页码：2711-2726
• 全文大小：783 KB
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• 作者单位：Wenhai Qi (1)
  Xianwen Gao (1)
  
  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China
  
• 刊物类别：Engineering
• 刊物主题：Electronic and Computer Engineering
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5878

文摘

This paper deals with the problem of \(L_1\) control for positive Markovian jump systems with time-varying delays and partly known transition rates. Firstly, by the use of appropriate co-positive type Lyapunov function, sufficient conditions for stochastic stability of positive Markovian jump systems with time-varying delays and partly known transition rates are proposed. Then, \(L_1\)-gain performance of the system considered is analyzed. Based on the results obtained, a state feedback controller is constructed such that the closed-loop Markovian jump system is positive and stochastically stable with \(L_1\)-gain performance. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results.