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Stability and Controller Design of Discrete-time Switched Systems Based on Transferring-dependent Lyapunov Function Approach

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  • Control Theory and Applications
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Abstract

This paper studies stability and controller design for discrete-time switched systems with unstable subsystems under the slow/fast admissible edge-dependent average dwell time (AED-ADT) switching. Different from the previous research results, it is the first time to propose transferring-dependent convex Lyapunov function (CLF) and transferring-dependent Lyapunov function (LF). Then, considering a slow/fast AED-ADT switching scheme, some excellent stability criteria are established according to transferring-dependent CLF and transferring-dependent LF, which have less restrictiveness compared with existing results. Corresponding to the novel transferring-dependent LFs and the properties of slow/fast AED-ADT switching, the new transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC) are devised to stabilize the underlying system. Finally, the effectiveness of the proposed approach is verified by two numerical examples.

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Author information

Authors and Affiliations

  1. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, Shandong, 266520, China

    Fu-Peng Li & Rui-Hua Wang

  2. School of Automation, Southeast University, Nanjing, Jiangsu, 210096, China

    Shu-Min Fei

Authors
  1. Fu-Peng Li
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  2. Rui-Hua Wang
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  3. Shu-Min Fei
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Corresponding author

Correspondence to Rui-Hua Wang.

Additional information

Fu-Peng Li received his B.S. degree in electrical engineering and automation from ShanDong JiaoTong University, Jinan, China in 2019. He is now pursuing an M.S. degree in the School of Information and Control Engineering, Qingdao, China. His research interests include switched system.

Rui-Hua Wang received her M.S. degree in operational research from Qufu Normal University, Qufu, China, in 2012 and a Ph.D. degree in control theory and control engineering from Southeast University, Nanjing, China, in 2016. She is currently a lecturer at the Qingdao University of Technology, Qingdao, China. Her research interests include hybrid systems, positive systems, fuzzy systems, tracking control, filtering and their applications. Her works have been widely published in international journals and conferences.

Shu-Min Fei received his Ph.D. degree in nonlinear systems at Beijing University of Aeronautics and Astronautics, Beijing, China, in 1995. From 1995 to 1997, he was a Postdoctoral Researcher with the Research Institute of Automation, Southeast University, China. He is currently a Professor with Southeast University, Nanjing, China. He has published more than 70 journal papers and his research interests include nonlinear systems, time delay system, complex systems, etc.

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Li, FP., Wang, RH. & Fei, SM. Stability and Controller Design of Discrete-time Switched Systems Based on Transferring-dependent Lyapunov Function Approach. Int. J. Control Autom. Syst. 20, 1142–1153 (2022). https://doi.org/10.1007/s12555-020-0891-x

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  • DOI: https://doi.org/10.1007/s12555-020-0891-x

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