Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay |
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| Affiliation: | 1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;2. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada;3. Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada;4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China;5. Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China;1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou 215021, China;2. Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai 201620, China;1. School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, PR China;1. School of Mathematics, Southeast University, Nanjing 210096, China;2. School of Mathematics and Computation Science, Anqing Normal University, 246133, China;3. School of Mathematics and Statistics, Yunnan Minzu University, Kunming, 650091, China |
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| Abstract: | This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods. |
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| Keywords: | Lur’e singularly perturbed systems Input-to-state stability (ISS) Linear matrix inequality (LMI) Time-delay systems |
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