Abstract
The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained.
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Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Hamid Reza Karimi. This work was supported in part by the National Natural Science Foundation of China (Grant no. 61374117, Grant no, 61004048, Grant no. 61174137, Grant no. 61104038 and Grant no. 61374086), the NSF of Jiang Su Province (Grant no. BK2010493), the grant from China Postdoctoral Science Foundation funded project 2012M510135, the Program for Changjiang Scholars and Innovative Research Team in University, the project form science & technology department of Sichuan province(Grant no. 2013GZ0080), the 973 project 2011CB707000.
Qunxian Zheng received the B.E. degree in biomedical engineering and M.S. degree in biophysics from University of Electronic Science and Technology of China, Chengdu, in 2008 and 2011, respectively. He is currently working towards a Ph.D. degree in circuits and systems at the University of Electronic Science and Technology of China, Chengdu. His research interests include fuzzy control and switched systems.
Hongbin Zhang received the BEng degree in aerocraft design from Northwestern Polytechnical University, Xian, China, in 1999, and the MEng and PhD degrees in circuits and systems from the University of Electronic Science and Technology of China, Chengdu, in 2002 and 2006, respectively. He has been with the School of Electrical Engineering, University of Electronic Science and Technology of China, since 2002, where he is currently a professor. From August 2008 to August 2010, he has served as a research fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. His current research interests include intelligent control, autonomous cooperative control and integrated navigation.
Dianhao Zheng received the B.E. degree in electronic science and technology from China University of Mining and Technology, Xuzhou, in 2009, and the M.S. degrees in circuits and systems from University of Electronic Science and Technology of China, Chengdu, in 2012. He is currently working towards a Ph.D. degree in circuits and systems at the University of Electronic Science and Technology of China, Chengdu. His research interests include cooperative control, multiagent systems, and switched systems.
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Zheng, Q., Zhang, H. & Zheng, D. Stability and asynchronous stabilization for a class of discrete-time switched nonlinear systems with stable and unstable subsystems. Int. J. Control Autom. Syst. 15, 986–994 (2017). https://doi.org/10.1007/s12555-016-0301-6
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DOI: https://doi.org/10.1007/s12555-016-0301-6