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Lyapunov Stability of Fuzzy Discrete Event Systems

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Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence (ICIC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4682))

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Abstract

Fuzzy discrete event systems (FDESs) as a generalization of (crisp) discrete event systems (DESs) may better deal with the problems of fuzziness, impreciseness, and subjectivity. Qiu, Cao and Ying, Liu and Qiu interestingly developed the theory of FDESs. As a continuation of Qiu’s work, this paper is to deal with the Lyapunov stability of FDESs, some main results of crisp DESs are generalized. We formalize the notions of the reachability of fuzzy states defined on a metric space. A linear algorithm of computing the r-reachable fuzzy state set is presented. Then we introduce the definitions of stability and asymptotical stability in the sense of Lyapunov to guarantee the convergence of the behaviors of fuzzy automaton to the desired fuzzy states when system engages in some illegal behaviors which can be tolerated. In particular, we present a necessary and sufficient condition for stability and another for asymptotical stability of FDESs.

This work was supported in part by the National Natural Science Foundation under Grant 90303024 and Grant 60573006, and the Research Foundation for the Doctorial Program of Higher School of Ministry of Education under Grant 20050558015 of China.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Zhongshan University, Guangzhou 510275, China

    Fuchun Liu & Daowen Qiu

  2. Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China

    Fuchun Liu

Authors
  1. Fuchun Liu
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  2. Daowen Qiu
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Editor information

De-Shuang Huang Laurent Heutte Marco Loog

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© 2007 Springer-Verlag Berlin Heidelberg

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Liu, F., Qiu, D. (2007). Lyapunov Stability of Fuzzy Discrete Event Systems. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_73

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  • DOI: https://doi.org/10.1007/978-3-540-74205-0_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74201-2

  • Online ISBN: 978-3-540-74205-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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