Stability analysis of switched homogeneous time-delay systems under synchronous and asynchronous commutation |
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| Institution: | 1. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shanxi 710049, China;2. School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China;1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan\n250014, PR China;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St John’s A1C5S7, Canada;3. Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, Shandong Normal University, Jinan, PR China;4. School of Mathematics, Southeast University, Nanjing 210096, PR China;5. University of Carthage, Faculty of Sciences of Bizerta, Department of Mathematics, Research Units of Mathematics and Applications UR13ES47, Zarzouna, Bizerta 7021, Tunisia;1. Department of Mathematics, Faculty of Basic Science, University of Mining and Geology, Hanoi, Vietnam;2. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Hanoi, Vietnam\n |
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| Abstract: | In this work, stability analysis for a class of switched nonlinear time-delay systems is performed by applying Lyapunov–Krasovskii and Lyapunov–Razumikhin approaches. It is assumed that each subsystem in the family is homogeneous (of positive or negative degree) and asymptotically stable in the delay-free setting. The cases of existence of a common or multiple Lyapunov–Krasovskii functionals and a common Lyapunov–Razumikhin function are explored. The scenarios with synchronous and asynchronous switching are considered, and it is demonstrated that depending on the kind of commutation, one of the frameworks for stability analysis outperforms another, but finally leading to similar restrictions for both types of switching (despite the asynchronous one seems to be more demanded). The obtained results are applied to mechanical systems having restoring forces with real-valued powers. |
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| Keywords: | Switched systems Time-delay systems Homogeneous systems Lyapunov–Krasovskii approach Lyapunov–Razumikhin approach |
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