Impulsive systems with hybrid delayed impulses: Input-to-state stability |
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| Institution: | 1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, PR China;2. School of Automation and Electrical Engineering, Linyi University, Linyi 276005, PR China;3. Department of Mathematics, Bharathiar University, Coimbatore 641046, Tamil Nadu, India;1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, PR China;2. Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, Shandong Normal University, Ji’nan, 250014, PR China;1. School of Automation, Guangdong University of Technology, Guangzhou 510006, PR China;2. School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, PR China |
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| Abstract: | This paper investigates input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems with hybrid delayed impulses. Based on Lyapunov method, some sufficient conditions ensuring ISS and iISS of impulsive systems are obtained, where the time derivative of Lyapunov function is indefinite, and the hybrid effects of delayed impulses are also fully considered. It is shown that the impulsive system is ISS provided that the combined action of time delay existing in impulses, continuous dynamic, and the cumulative strength of hybrid impulses satisfies some conditions, even if the hybrid delayed impulses play a destabilizing effect on ISS. Examples and their simulations are presented to illustrate the applicability of the proposed results. |
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| Keywords: | Impulsive systems Input-to-state stability Lyapunov method Hybrid delayed impulses Indefinite derivative |
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