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A survey on Markovian jump systems: Modeling and design

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Abstract

Markovian jump systems are a special class of hybrid and stochastic systems which can be used to describe many real world applications, such as manufacturing systems, power systems, chemical systems, economic systems, communication and control, etc. In this paper, a survey on recent developments of modeling, analysis and design of Markovian jump systems is presented. First, stability issues on Markovian jump systems are addressed. Then a variety of control and filter design methods are systematically recalled. Furthermore, the new trends of Markovian jump systems with uncertain transition rates as well as semi-Markovian jump systems are also discussed.

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Authors and Affiliations

  1. School of Electrical and Electronic Engineering, the University of Adelaide, Adelaide, SA, 5005, Australia

    Peng Shi

  2. College of Engineering and Science, Victoria University, Melbourne, VIC, 8001, Australia

    Peng Shi

  3. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, China

    Fanbiao Li

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  1. Peng Shi
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Correspondence to Peng Shi.

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Peng Shi received the BSc degree in Mathematics from Harbin Institute of Technology, China; the ME degree in Systems Engineering from Harbin Engineering University, China; the PhD degree in Electrical Engineering from the University of Newcastle, Australia; the PhD degree in Mathematics from the University of South Australia; and the DSc degree from the University of Glamorgan, UK. Dr Shi was a post-doctorate and lecturer at the University of South Australia; a senior scientist in the Defence Science and Technology Organisation, Australia; and a professor at the University of Glamorgan, UK. Currently, he is a professor at The University of Adelaide; and Victoria University. Dr Shi’s research interests include system and control theory, computational and intelligent systems, and operational research. Dr Shi is a Fellow of Institute of Electrical and Electronic Engineers, a Fellow of the Institution of Engineering and Technology, and a Fellow of the Institute of Mathematics and its Applications. He has been in the editorial board of a number of international journals, including IEEE Transactions on Automatic Control; IEEE Transactions on Fuzzy Systems; IEEE Transactions on Circuits and Systems-I: Regular Papers; IEEE Transactions on Cybernetics; and Automatica. Dr Shi now serves the Chair of Control, Aerospace and Electronic Systems Chapter, IEEE South Australia Section; and a College of Expert Member, Australian Research Council.

Fanbiao Li received the BSc degree in Applied Mathematics from Mudanjiang Normal University, China, in 2008, and the MSc degree in Operational Research and Cybernetics from Heilongjiang University, China, in 2012. Currently, he is pursuing for his PhD degree in the Department of Control Science and Engineering at Harbin Institute of Technology, China; and he is a Joint Training PhD Student with the School of Electrical and Electronic Engineering, the University of Adelaide, Australia. His research interests include stochastic systems, robust control and networked control systems. He is an active reviewer for many international journals.

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Shi, P., Li, F. A survey on Markovian jump systems: Modeling and design. Int. J. Control Autom. Syst. 13, 1–16 (2015). https://doi.org/10.1007/s12555-014-0576-4

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