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Abstract
This article investigates input-to-state stability (ISS) problem of asynchronous discrete-time impulsive switched delayed systems, in which switching and impulse may be asynchronous. A novel bounded admissible edge-dependent average dwell time (BAED-ADT) switching signal is designed. Based on this division rule of switching subsystems, we adopt the slow switching method for the stable subsystems and the fast switching method for the unstable subsystems, so that stable subsystems can compensate unstable subsystems. Combined with admissible edge-dependent average impulsive interval (AED-AII) impulsive signal, a new unified ISS stability result is established, which could be applied to impulsive switched systems with an arbitrary combination of unstable and stable subsystems. Without solving the linear matrix inequality, it is allowed to readjust the AED-ADT boundary of the newly proposed stability condition according to the actual impulsive and switching signal. Further, compared with the existing fruits, the new stability condition is an extension and improvement of the previous one, which is less conservative. Several numerical examples are provided to show the validity of the conditions and the advantages of the theoretic results.
Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China (62103231), Postgraduate Education Quality Improvement Plan Education Reform Project SDYJG21031.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The datasets generated and (or) analysed during the current study are available from the corresponding author on reasonable request.
Additional information
Notes on contributors
Mengjie Li
Mengjie Li received the B.S. degree in Information and Computing Sciences from School of Science, North University of China, Taiyuan, China, in June 2021. Since September 2021, she has been working toward the M.S. degree in Operations Research and Cybernetics from School of Engineering, Qufu Normal University, Rizhao, China. Her research interests include impulsive switched systems, time-delay systems.
Zihan Liu
Zihan Liu received the B.S. degree from Qingdao University of Science and Technology in 2020. She is currently studying for a M.S. degree in Qufu Normal University. Her current research interests include impulsive switched systems, event-triggered control.
Tao Sun
Tao Sun is studying for a bachelor’s degree in Automation from School of Engineering, Qufu Normal University, Rizhao, China. His current interests include automation control theory, data mining, Matlab simulation.
Lijun Gao
Lijun Gao received the M.S. and Ph.D. degrees in automation from Qufu Normal University, China in 2004 and 2007, respectively. She is currently a Professor at Institute of Automation, Qufu Normal University. Her current research interests include switched systems, impulsive control, Markov jump systems.