Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

Yufang Chang; Guisheng Zhai; Bo Fu; Lianglin Xiong

doi:10.1109/JAS.2019.1911681

Volume 6 Issue 5

Sep. 2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2019 > 6(5): 1116-1126

Yufang Chang, Guisheng Zhai, Bo Fu and Lianglin Xiong, "Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1116-1126, Sept. 2019. doi: 10.1109/JAS.2019.1911681

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Yufang Chang, Guisheng Zhai, Bo Fu and Lianglin Xiong, "Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1116-1126, Sept. 2019. doi: 10.1109/JAS.2019.1911681

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Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

doi: 10.1109/JAS.2019.1911681

Funds: This work was supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (C) (21560471), the Green Industry Leading Program of Hubei University of Technology (CPYF2017003), and the National Natural Science Foundation of China (11601474, 11461082)

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Author Bio:
Yufang Chang (M’16) received the B.Eng. degree in automation from Wuhan University of Technology, Wuhan, China, in 2001. She received the M.A.Sc degree in control science and engineering from Wuhan University of Technology, and Ph.D. degree in traffic information engineering and control from Wuhan University of Technology, Wuhan, China, in 2004 and 2013, respectively. From 2004 to 2013, she was a Lecturer at Hubei University of Technology. Since 2014, she has been an Associate Professor with the School of Electrical and Electronic Engineering, Hubei University of Technology. She is the author of more than 25 articles, and more than 10 inventions. Her research interests include controller design, switched systems, energy system modeling and simulation, optimization theory and application

Guisheng Zhai (M’98–SM’01) received the B.S degree from Fudan University, China, in 1988, and received the M.E and Ph.D degrees, both in system science, from Kobe University, Japan, in 1993 and 1996, respectively. After two years of industrial experience, Dr. Zhai moved to Wakayama University, Japan, in 1998, and then to Osaka Prefecture University, Japan, in 2004. He held visiting professor positions at University of Notre Dame from August 2001 to July 2002, and at Purdue University from March 2016 through February 2017. In April 2010, he joined the faculty of Shibaura Institute of Technology, Japan, where he currently is a Full Professor of mathematical sciences. His research interests include large scale and decentralized control systems, robust control, switched systems and switching control, networked control and multi-agent systems, neural networks, and signal processing. Dr. Zhai is on the editorial board of several academic journals including IET Control Theory & Applications, International Journal of Applied Mathematics and Computer Science, Journal of Control and Decision, Frontiers of Mechanical Engineering, and International Journal of Computing Science and Applied Mathematics. He is a Senior Member of IEEE, a member of ISCIE, SICE, JSST and JSME

Bo Fu received the Ph.D. degree in water conservancy and hydropower engineering in 2006 from Huazhong University of Science and Technology, Wuhan, China. He is a Professor at the School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan, China. His research interests include control theory and control engineering, pattern recognition

Lianglin Xiong received the B.Sc. degree in mathematics and applied mathematics from Neijiang Normal University, Sichuan, China, in 2004. He received the M.Sc. and D.Sc. degrees both in applied mathematics from University of Electronic Science and Technology of China, Chengdu, China, in 2007 and 2009, respectively. He is on the staff board of School of Mathematics and Computer Science, Yunnan Minzu University, from March 2010 to the present. In 2012, he was appointed as a Professor and master tutor of applied mathematics. His research interests include stability analysis and controller design for functional differential systems such as neutral delayed systems, neural networks, Lur’e systems, switched systems, and Markovian jump systems
Corresponding author: G. Zhai is with the Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan (e-mail: zhai@shibaura-it.ac.jp)
Received Date: 2019-05-07
Accepted Date: 2019-07-10

Available Online: 2019-07-19

Abstract

Abstract

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an output-dependent switching law by constructing a robust Luenberger observer for each subsystem.

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Highlights

Quadratic stabilization is studied for a class of switched linear systems with norm bounded uncertainties.
A new concept “convex Hurwitz combination with L2 disturbance attenuation” is proposed for quadratic stabilization of switched uncertain linear systems.
When a convex combination of subsystems is quadratically stable, a state-dependent switching law is proposed such that the entire switched linear system is quadratically stable.
When a convex combination of subsystems is quadratically stable, and in addition a robust detectability condition holds for all subsystems, a robust Luenberger observer is constructed for each subsystem, and an output-dependent switching law is proposed to quadratically stabilize the switched uncertain linear system.
The feasibility of the convex combination condition, the switching law implementation and the associated observer can be checked by using standard LMI approach.

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

doi: 10.1109/JAS.2019.1911681

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通讯作者: 陈斌, bchen63@163.com

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