Limit equation of fuzzy relation and its application

Chengjia Li, Victor M. Becerra

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    Mamdani proposed the first fuzzy controller, which was described by fuzzy linguistic rules and fuzzy relations. The stability of this type fuzzy controller is closely related to fuzzy relations. In this paper, a limit equation is first deduced from the stability conditions of generalized fuzzy control systems. Next, the structure of the solutions to the limit equation and the existence of minimal solution are discussed. Minimal solutions can be obtained by a path analysis based method. The minimal solutions of the limit equation produce elementary stable matrix forms, which are useful to analyze the stability of closed loop fuzzy systems. An example from the level control of water tank illustrates the proposed method.
    Original languageEnglish
    Title of host publicationIEEE International Conference on Systems, Man and Cybernetics, 2004
    Place of PublicationPiscataway
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages3383 - 3388
    ISBN (Print)0780385667
    Publication statusPublished - 2004


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