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A Fuzzy Control Approach to Stabilization of Markovian Jump Systems with General Unknown Transition Probabilities

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Abstract

This paper is devoted to the investigation of the stability and stabilization problems for a class of Markovian jump nonlinear systems with general unknown transition rates (GUTRs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is utilized to characterize the Markovian jump nonlinear systems with general unknown transition probabilities. Some sufficient criteria on stochastic stability are derived in terms of linear matrix inequalities, and a mode-dependent fuzzy controller is designed. The derived results extend the conclusions recently presented by Sheng and Gao (Stabilization for Markovian jump nonlinear systems with partly unknown transition probabilities via fuzzy control, Fuzzy Set Syst 161(21): 2780–2792, 2010). In fact, the system discussed in Sheng and Gao (Fuzzy Set Syst 161(21) 2780–2792, 2010) is a special case of ours, because their transition rates are completely known or completely unknown, while in our GUTR T-S fuzzy model, each transition rate can be completely unknown or only its estimate value is known. Finally, a numerical example is present to illustrate the effectiveness and applicability of the proposed method.

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Acknowledgments

This research is supported by the National Natural Science Foundations of China (61473097) and National 863 Plan Project (2008 AA04Z401, 2009 AA043404).

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Authors and Affiliations

  1. Software Institute, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Lei Shi

  2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, People’s Republic of China

    Yonggui Kao

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  1. Lei Shi
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Correspondence to Yonggui Kao.

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Shi, L., Kao, Y. A Fuzzy Control Approach to Stabilization of Markovian Jump Systems with General Unknown Transition Probabilities. Int. J. Fuzzy Syst. 18, 1–11 (2016). https://doi.org/10.1007/s40815-015-0114-4

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  • DOI: https://doi.org/10.1007/s40815-015-0114-4

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