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Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: Partially known transition probabilities case

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Abstract

This paper focuses on the stability analysis and the stabilization problem for a discrete-time Markovian jump fuzzy systems (MJFSs) with time-varying delays and partially known transition probabilities. These systems are made more general, by relaxing the traditional assumption in MJFSs that all the transition probabilities must be completely known. The class of MJFSs considered is described by a fuzzy model composed of two levels: a crisp level that represents the jumps and a fuzzy level that represents the system nonlinearities. Based on a stochastic Lyapunov function, stability and stabilization conditions for the MJFSs with time-varying delays are derived in both the case of completely known transition probabilities and the case of partially known transition probabilities. The derived conditions are represented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the effectiveness of the proposed theorem.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Yonsei University, Seodaemun-gu, Seoul, 120-749, Korea

    Min Kook Song & Jin Bae Park

  2. Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Chonbuk, 573-701, Korea

    Young Hoon Joo

Authors
  1. Min Kook Song
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  2. Jin Bae Park
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Corresponding author

Correspondence to Jin Bae Park.

Additional information

Recommended by Editorial Board member Shengyuan Xu under the direction of Editor Hyungbo Shim.

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.:2012014088) and the Human Resources Development program( No. 20124030200040) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy.

Min Kook Song received his B.S. and M.S. degrees in Electrical and Electronic Engineering from Yonsei University, Seoul, Korea, in 2006 and 2007, respectively. He is currently working toward a Ph.D. degree in Electrical and Electronic Engineering at the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea. His research interests include fuzzy control and filtering, nonlinear control, networked control system, neural networks, and genetic algorithms.

Jin Bae Park received his B.E. degree in Electrical Engineering from Yonsei University, Seoul, Korea, and his M.S. and Ph.D. degrees in Electrical Engineering from Kansas State University, Manhattan, in 1977, 1985, and 1990, respectively. Since 1992, he has been with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, where he is currently a professor. His research interests include robust control and filtering, nonlinear control, intelligent mobile robot, fuzzy logic control, neural networks, and genetic algorithms. He served as Editor-in-Chief of the International Journal of Control, Automation, and Systems (IJCAS) (2006–2010) and has been serving as the President of the Institute of Control, Robotics, and Systems (ICROS) in 2013.

Young Hoon Joo received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a professor in the Department of Control and Robotics Engineering, Kunsan National University, Korea. His major interest is mainly in the field of intelligent robot, intelligent control, and human-robot interaction. He served as President for Korea Institute of Intelligent Systems (KIIS) (2008–2009) and is serving as Editor for the International Journal of Control, Automation, and Systems (IJCAS) (2008-present) and is serving as the Vice-President for the Korean Institute of Electrical Engineers (KIEE) (2012-present).

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Song, M.K., Park, J.B. & Joo, Y.H. Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: Partially known transition probabilities case. Int. J. Control Autom. Syst. 11, 136–146 (2013). https://doi.org/10.1007/s12555-011-9112-y

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  • DOI: https://doi.org/10.1007/s12555-011-9112-y

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