Lyapunov Stability of Fuzzy Discrete Event Systems

  • Authors:

  • Fuchun Liu;Daowen Qiu

  • Affiliations:

  • Department of Computer Science, Zhongshan University, Guangzhou 510275, China and Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510090, China;Department of Computer Science, Zhongshan University, Guangzhou 510275, China

  • Venue:
  • ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
  • Year:
  • 2009

Quantified Score

Hi-index 0.01

Visualization

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.