Stability analysis for a class of switched systems with state constraints via time-varying Lyapunov functions |
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| Institution: | 1. Collegee of Science, Hebei North University, Zhangjiakou, 075000, PR China;2. School of Information and Control Engineering, China University of Mining and Technology, Xuzhou, 221116, PR China;1. Univ. Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, Grenoble 38000, France;2. Institut National des Sciences Appliquées de Lyon, Ampère lab, Lyon F-59000, France;3. University of Orlans, INSA Centre Val de Loire (CVL), PRISME, EA, 4229, Orléans, France;1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China;2. School of Electronics and Information Engineering, Suzhou University of Science and Technology, Suzhou 215000, China;1. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;2. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;1. Departamento de Automação e Sistemas, Universidade Federal de Santa Catarina, Florianópolis, Brazil;2. Université Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering, Univ. Grenoble Alpes), GIPSA-Lab, Grenoble 38000, France;3. Université de Lorraine, CNRS, CRAN, Nancy F-54000, France;1. Department of Mathematics, Faculty of Sciences, University of Zagreb, Zagreb, Croatia;2. LARIAT – Laboratory for Intelligent Autonomous Systems & RIT Croatia, Dubrovnik, Croatia;3. Department of Mathematics, J. J. Strossmayer University of Osijek, Osijek, Croatia;4. LARIAT – Laboratory for Intelligent Autonomous Systems, University of Dubrovnik, Croatia |
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| Abstract: | This article investigates the stability analysis for a class of continuous-time switched systems with state constraints under pre-specified dwell time switchings. The state variables of the studied system are constrained to a unit closed hypercube. Firstly, based on the definition of set coverage, the system state under saturation is confined to a convex polyhedron and the saturation problem is converted into convex hull. Then, sufficient conditions are derived by introducing a class of multiple time-varying Lyapunov functions in the framework of pre-specified dwell time switchings. Such a dwell time is an arbitrary pre-specified constant which is independent of any other parameters. In addition, the proposed Lyapunov functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functions at switching instants. The feature of this paper is that the definition of set coverage is utilized to replace the restriction on the row diagonally dominant matrices with negative diagonal elements to analyze stability. The other feature of the constructed time-varying Lyapunov functions is that there are two time-varying functions. One of the two time-varying functions contains the jump rate, which will present a certain degree of freedom in designing the dwell time switching signal. An iterative linear matrix inequality (LMI) algorithm is presented to verify the sufficient conditions. Finally, two examples are presented to show the validity of the method. |
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