ABSTRACT
This paper is concerned with the model reduction problem for discrete-time periodic systems with time-varying delay. By utilising an adjusted reciprocally convex combination approach, some sufficient criteria are established to guarantee that the discrete-time periodic system with time-varying delay is asymptotically stable. Then, the reduced-order model is designed to approximate the original system. In the design, both the dissipativity and the Hankel norm performances are considered to test the model approximation, and correspondingly, the conditions are also established, which guarantee that the approximation error system is asymptotically stable with the dissipativity performance and the Hankel norm property, respectively. The convex linearisation and the projection are presented to design the reduced-order model, respectively. Finally, numerical examples are provided to verify the effectiveness of the design scheme.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Liu Yang
Liu Yang received the B.S. degree in Computer Science and Technology from Harbin University, China in 2012; the M.E. degree in Mathematics from Heilongjiang University in 2016; She is currently working toward the PH.D. degree in Control Science and Engineering from Harbin Engineering University, China. Her current research interests include periodic system, networked control systems.
Chengwei Wu
Chengwei Wu received the B.S. degree in management from the Arts and Science College, Bohai University, Jinzhou, China, in 2013, and the M.S. degree from Bohai University, in 2016. He is currently pursuing the Ph.D. degree with the Harbin Institute of Technology, Harbin, China. From July 2015 to December 2015, he was a Research Assistant with the Department of Mechanical Engineering, The Hong Kong Polytechnic University. His research interests include fuzzy control, adaptive control, sliding mode control, and networked control systems.
Yuxin Zhao
Yuxin Zhao received the Ph.D. degree in navigation, guidance, and control from Harbin Engineering University, China, in 2005. He completed the postdoctorial research in control science and engineering from the Harbin Institute of Technology, China, in 2008. In 2004, he was awarded scholarship of the State Administration of Foreign Experts Affairs for visiting Levin Institute of State University of New York, and from 2012 to 2013, he visited the Centre for Transport Studies, Imperial College London, as a Research Scholar.
Ligang Wu
Ligang Wu received the B.S. degree in Automation from Harbin University of Science and Technology, China in 2001; the M.E. degree in Navigation Guidance and Control from Harbin Institute of Technology, China in 2003; the Ph.D. degree in Control Theory and Control Engineering from Harbin Institute of Technology, China in 2006. From January 2006 to April 2007, he was a Research Associate in the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong. From September 2007 to June 2008, he was a Senior Research Associate in the Department of Mathematics, City University of Hong Kong, Hong Kong. From December 2012 to December 2013, he was a Research Associate in the Department of Electrical and Electronic Engineering, Imperial College London, London, UK. In 2008, he joined the Harbin Institute of Technology, China, as an Associate Professor, and was then promoted to a Professor in 2012.