Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales |
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| Authors: | Vipin Kumar Mohamed Djemai Michael Defoort Muslim Malik |
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| Institution: | 1. School of Basic Sciences, Indian Institute of Technology Mandi, H. P. India;2. LAMIH, CNRS, UMR-8201, INSA HdF UPHF, Valenciennes 59313, France;1. School of Basic Sciences, Indian Institute of Technology Mandi, Kamand (H.P.) 175 005, India;2. Department of Mathematics, Guelma University, Guelma 24000, Algeria;1. School of Engineering, Qufu Normal University, Rizhao, Shandong 276826, PR China;2. School of Information Science and Engineering, Qufu Normal University, Rizhao, Shandong 276826, PR China;3. School of Information and Engineering, Yangzhou University, Yangzhou, Jiangsu 225009, PR China;1. School of Science, Jimei University, Xiamen 361021, China;2. Department of Mathematics, Texas A&M University at Qatar, Doha, Qatar;3. School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China;4. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China;1. Department of Mathematics, Washington College, 300 Washington Avenue, Chestertown, MD 21620-5129, United States;2. Université Polytechnique Hauts-de-France, LAMIH, CNRS UMR 8201, Valenciennes 59313, France |
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| Abstract: | In this article, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary time domain. This problem is formulated using time scale theory where the time domain can be continuous, discrete, union of disjoint intervals with variable gaps and variable lengths or any combination of these. Using common Lyapunov-quadratic and Lyapunov-like functions, we establish sufficient conditions to ensure the FTS results. Further, to solve the stabilization problem, we design state feedback controllers. We have illustrated the effectiveness of the obtained analytical results though numerical examples. |
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