Stabilization of discrete-time switched singular time-delay systems under asynchronous switching |
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| Authors: | Jinxing Lin Shumin Fei Zhifeng Gao |
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| Institution: | 1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, PR China;2. Key Laboratory of Measurement and Control of CSE (School of Automation, Southeast University), Ministry of Education, Nanjing 210096, PR China;1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China;2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China;3. College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, 266580, China;1. Department of Sciences, Pontificia Universidad Católica del Perú PUCP, Lima, Peru;2. Department of Applied Mathematics and Statistics, University of São Paulo at São Carlos, Brazil;3. Department of Electrical Engineering, University of São Paulo at São Carlos, Brazil;1. Department of Sciences, Pontificia Universidad Católica del Perú PUCP, Lima, Peru;2. Department of Applied Mathematics and Statistics, University of São Paulo at São carlos, Brazil;3. Department of Electrical Engineering, University of São Paulo at São Carlos, Brazil;1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China;2. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway;1. College of Information and Control Engineering, China University of Petroleum, Qingdao, 266555, China;2. School of Engineering and Science, Victoria University, Melbourne, Vic 8001, Australia;3. School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia;4. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, China |
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| Abstract: | This paper is concerned with the problem of state feedback stabilization of a class of discrete-time switched singular systems with time-varying state delay under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the subsystems. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of a class of stabilizing switching laws is first derived to guarantee the closed-loop system to be regular, causal and exponentially stable in the presence of asynchronous switching. The stabilizing switching laws are characterized by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method. |
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