Absolute exponential stability and stabilization of switched nonlinear systems |
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| Affiliation: | 1. School of Mathematical Sciences, University of Jinan, Jinan 250022, Shandong, China;2. Institute of Automation, Qufu Normal University, Qufu 273165, Shandong, China;1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;2. Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing 210094, China;3. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China;4. Department of Computer Science, Brunel University London, Uxbridge, Middlesex UB8 3PH, United Kingdom;5. Department of Mathematics, Yangzhou University, Yangzhou 225002, China;6. Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | This paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are Metzler. Nonlinearity of the systems is constrained in a sector field, which is bounded by two odd symmetric piecewise linear functions. Multiple Lyapunov functions are introduced to deal with the stability of such nonlinear systems. Compared with some existing results obtained by the common Lyapunov function approach in the literature, the conservatism of our results is reduced. All present conditions can be solved by linear programming. Furthermore, the absolute exponential stabilization for the considered systems is designed by the state-feedback and average dwell time switching strategy. Two examples are also given to illustrate the validity of the theoretical findings. |
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| Keywords: | Absolute exponential stability Switched nonlinear systems Multiple Lyapunov functions Average dwell time switching |
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