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ABSTRACT
In this paper, the stabilisation problem for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance is addressed. First, by proposing a time-scheduled multiple linear copositive Lyapunov function which is time-varying during the mode-dependent minimum dwell-time interval, sufficient conditions of asymptotical stability for positive switched T-S fuzzy delayed system under dwell-time switching are derived for the first time. Then, sufficient conditions for the underlying system to be asymptotically stable with standard L1 and L∞ performance are obtained, respectively. Based on the obtained results, a fuzzy state-feedback controller scheme is designed to stabilise the positive switched T-S fuzzy delayed system, while guaranteeing the positivity and asymptotical stability with standard L1 performance in closed loop. Furthermore, the stabilisation problem under standard L∞ performance is also solved. All the results are presented in the linear programming form. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 61273120, 61673219), Six Talents Peaks Project of Jiangsu Province (No. XNYQC-CXTD-001), and Tianjin Major Projects of Science and Technology (No. 15ZXZNGX00250).
Disclosure statement
No potential conflict of interest was reported by the authors.
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Notes on contributors
Shuo Li
Shuo Lireceived her B.S. degree in Automation from Hangzhou Dianzi University, Hangzhou, China, in 2012. She received her Ph.D. degree in Control Theory and Control Engineering at School of Automation, Nanjing University of Science and Technology, Nanjing, China, in 2017. She was appointed as Lecturer in 2017 at Hangzhou Dianzi University. Her main research interests include positive systems, switched systems, nonlinear systems, fuzzy systems and their applications.
Zhengrong Xiang
Zhengrong Xiangreceived his Ph.D. degree in Control Theory and Control Engineering at Nanjing University of Science and Technology, Nanjing, China, in 1998. Since 1998 he has been faculty member and he is currently full professor at Nanjing University of Science and Technology. He was appointed as Lecturer in 1998 and Associate Professor in 2001 at Nanjing University of Science and Technology. He is a member of the IEEE, member of the Chinese Association for Artificial Intelligence. His main research interests include switched systems, nonlinear control, robust control, and networked control systems.
Jian Guo
Jian Guoreceived his PhD degree in Control Theory and Control Engineering at Nanjing University of Science and Technology, Nanjing, China, in 2002. Since 2002 he has been faculty member and he is currently full professor at Nanjing University of Science and Technology. He was appointed as lecturer in 2002 and associate professor in 2005 at Nanjing University of Science and Technology. He is a member of the Chinese Association of Automation. His main research interests include nonlinear systems, motion control and adaptive robust control.