Abstract
This paper investigates the stabilization problem of nonlinear switched systems subject to the distributed time-delay. The considered nonlinear switched systems are quite general whose dynamics are affected by both exogenous noises and distributed time-delay. The purpose of the addressed problem is to propose a state feedback control law such that, the closed-loop system is exponentially stable in the mean square sense and meanwhile, the required weighted L2 gain is achieved. By resorting to the Lyapunov functional method in combination with the average dwell time approach, sufficient conditions are provided for the existence of the desired control scheme in terms of the feasibility of certain Hamilton-Jacobi inequalities (HJIs). Within the established framework, the required feedback controller gains can be obtained by solving the series of HJIs. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the developed control algorithm.
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This work was supported in part by the National Natural Science Foundation of China under Grants 61773209 and 61973163, and the Natural Science Foundation of Jiangsu Province under Grant BK 20190021.
Chaochen Wang received his B.S. degree in automation from Nanjing University of Science and Technology in 2010. His research interests include nonlinear control, signal processing and navigation.
Xiaoli Fang received her B.S. degree in automation from Jinan University in 2018. Her research interests include nonlinear systems and intelligent control.
Lifeng Ma received his B.Sc. degree in Automation from Jiangsu University, Zhenjiang, China, in 2004 and a Ph.D. degree in control science and engineer ing from Nanjing University of Science and Technology, Nanjing, China, in 2010. From August 2008 to February 2009, he was a visiting Ph.D. student in the Department of Information Systems and Computing, Brunel University London, U.K. From January 2010 to April 2010 and May 2011 to September 2011, he was a research associate in the Department of Mechanical Engineering, the University of Hong Kong. From March 2015 to February 2017, he was a visiting research fellow at the King’s College London, U.K. He is currently a professor in the School of Automation, Nanjing University of Science and Technology, Nanjing, China. His current research interests include nonlinear control and signal processing, variable structure control, distributed control and filtering, time-varying systems and multi-agent systems. He has published more than 20 papers in refereed international journals. He serves as an editor for Neurocomputing and International Journal of Systems Science. He is a very active reviewer for many international journals.
Jie Zhang received his B.Sc. degree in automatic control in 2002, an M.Sc. degree in automatic control in 2004 and a Ph.D. degree in control theory and control engineering in 2011, all from Nanjing University of Science and Technology, Nanjing, China. From April 2013 to March 2014, he was an academic visitor in the Department of Information Systems and Computing, Brunel University London, UK. He is currently a professor in the School of Automation, Nanjing University of Science and Technology. His current research interests include stochastic systems, networked systems, stochastic control and neural networks.
Yuming Bo received his B.Sc. degree in automatic control in 1984, an M.Sc. degree in automatic control in 1987 and a Ph.D. degree in control theory and control engineering in 2005, all from Nanjing University of Science and Technology, Nanjing, China. He is now a professor of Control Theory and Control Engineering in the School of Automation at Nanjing University of Science and Technology, Nanjing, China. His research interests include stochastic control and estimation, computer communication and programming. He has published more than 50 papers in referred journals and served as an associate editor for two journals.
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Wang, C., Fang, X., Ma, L. et al. Stabilization of Nonlinear Switched Systems with Distributed Time-delay: The Discrete-time Case. Int. J. Control Autom. Syst. 19, 3843–3852 (2021). https://doi.org/10.1007/s12555-020-0308-x
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DOI: https://doi.org/10.1007/s12555-020-0308-x