Stability and \({L_{\infty }}\) -Gain Analysis for Positive Switched Systems with Time-Varying Delay Under State-Dependent Switching

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• 作者：Shuo Li ; Zhengrong Xiang
• 关键词：Positive systems ; Switched systems ; Exponential stability ; $${L_\infty }$$ L ∞ ; gain performance ; Time ; varying delay ; State ; dependent switching
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：35
• 期：3
• 页码：1045-1062
• 全文大小：990 KB
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• 作者单位：Shuo Li (1)
  Zhengrong Xiang (1)
  
  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of 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 investigates the problems of stability and \({L_\infty }\)-gain analysis for a class of positive switched systems with time-varying delay. Attention is focused on designing a state-dependent switching rule such that the system satisfies a prescribed \({L_\infty }\)-gain performance level, where the proposed scheme does not require the switching instants to be known in advance. By constructing an appropriate co-positive type Lyapunov–Krasovskii functional, sufficient conditions for exponential stability with \({L_\infty }\)-gain performance of the underlying systems are derived. Furthermore, the stability along the switching surface is analyzed. Finally, two examples are presented to demonstrate the effectiveness of the proposed method. Keywords Positive systems Switched systems Exponential stability \({L_\infty }\)-gain performance Time-varying delay State-dependent switching