Stability and stabilization of a class of nonlinear impulsive hybrid systems based on FSM with MDADT |
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| Affiliation: | 1. School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, PR China;2. School of Energy and Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China;3. School of Environmental and Biological Science and Technology, Dalian University of Technology, Dalian, Liaoning 116012, PR China;1. Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands;2. Systems & Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;1. College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, PR China;2. Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, PR China |
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| Abstract: | The issue of stability and stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM) with mode-dependent average dwell time (MDADT) is investigated in this paper. The concepts of global asymptotic stability and global exponential stability are extended for the systems, and the multiple Lyapunov functions (MLFs) are constructed to prove the sufficient conditions of global asymptotic stability and global exponential stability, respectively. Furthermore, the method of stabilization is also given for the hybrid systems. The application of MLFs and MDADT leads to a reduction of conservativeness in contrast with classical Lyapunov function. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed approach. |
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| Keywords: | FSM MDADT Hybrid systems MLFs Global exponential stability |
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