Limit equation of fuzzy relation and its application

Author

Li, Chenglia ; Becerra, V.M.

Author_Institution

Sch. of Sci., Hangzhou Dianzi Univ., China

Volume

4

fYear

2004

fDate

10-13 Oct. 2004

Firstpage

3383

Abstract

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.

Keywords

closed loop systems; fuzzy control; fuzzy set theory; stability; closed loop fuzzy system; fuzzy control; fuzzy linguistic rules; fuzzy relation; limit equation; minimal solution; path analysis; stability analysis; water tank level control; Analytical models; Closed loop systems; Control systems; Equations; Fuzzy control; Fuzzy logic; Fuzzy set theory; Fuzzy systems; Stability analysis; Takagi-Sugeno model;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man and Cybernetics, 2004 IEEE International Conference on

ISSN

1062-922X

Print_ISBN

0-7803-8566-7

Type

conf

DOI

10.1109/ICSMC.2004.1400865

Filename

1400865