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ABSTRACT
This paper considers the problems of stochastic stability analysis and distributed output-feedback controllers design for Markovian jump systems interconnected over an undirected graph with state time-varying delay. Specifically, a sufficient condition for the well-posedness, stochastic stability and contractiveness of the resultant closed-loop system is first developed in the form of non-linear matrix inequalities. Then, to avoid the difficulty of solving non-linear matrix inequalities, the sufficient condition is relaxed to an equivalent one in terms of coupling linear matrix inequalities (LMIs), which provides an effective way to confirm the existence of a distributed output-feedback controller inheriting the structure of the given plant. Furthermore, a constructive algorithm is given for the design of such a distributed output-feedback controller to achieve the well-posedness, stochastic stability as well as the contractiveness of the corresponding closed-loop system. Finally, numerical simulations are given to illustrate the validity of the proposed method.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Xiaojuan Xue
Xiaojuan Xue is currently pursuing the Ph.D. degree at School of Science, Nanjing University of Science and Technology, Nanjing, China. Her research interests include systems interconnected over graphs, multidimension systems, and control theory. During the period between October 28, 2017 and October 28, 2018, she conducts research in Akita Prefectural University, Akita, Japan as a visiting student.
Huiling Xu
Huiling Xu received her B.Sc. degree in mathematics from the Nanjing University of Science and Technology, China in 1992, and the M.S. and Ph.D. degrees in control science and control engineering from the Nanjing University of Science and Technology, China in 1999 and 2005, respectively. From 2009 to 2011 she was a Research Fellow in the school of electrical and electronic engineering at the Nanyang Technological University (NTU), Singapore. Since Apr. 2012, she has been a Professor in the school of science at the Nanjing University of Science and Technology, China. Her current research interests include distributed control, multidimensional systems, singular systems, time-delay systems, modeling and optimization for big data analytics.
Li Xu
Li Xu received the B. Eng. degree from Huazhong University of Science and Technology, Wuhan, China, in 1982, and the M. Eng. and Dr. Eng. degrees from Toyohashi University of Technology, Toyohashi, Japan, in 1990 and 1993, respectively. From April 1993 to March 1998, he was an Assistant Professor at the Department of Knowledge-Based Information Engineering, Toyohashi University of Technology. From April 1998 to March 2000, he was a Lecturer at the Department of Information Management, Asahi University, Gifu, Japan. Since April 2000, he has been with the Faculty of Systems Science and Technology, Akita Prefectural University, Akita, Japan, where he is currently a Professor at the Department of Intelligent Mechatronics. His research interests include multidimensional system theory, signal processing and the applications of computer algebra to system theory. Dr. Xu was an Associate Editor from April 2000 to November 2014, and has been an Editorial Board Member since December 2014 for the international journal of Multidimensional Systems and Signal Processing (MSSP).