Linguistic stability analysis of fuzzy closed loop control systems

doi:10.1016/0165-0114(95)00229-4

Fuzzy Sets and Systems

Volume 82, Issue 1, 26 August 1996, Pages 27-34

https://doi.org/10.1016/0165-0114(95)00229-4 Get rights and content

Abstract

A linguistic analysis method for fuzzy closed loop control systems where both fuzzy controller and controlled processes are described by linguistic rules is proposed in this paper. First, a linguistic relation model of a fuzzy closed loop control system is deduced from the linguistic rule models of the fuzzy controller and the controlled process. Then the linguistic stability of the fuzzy closed loop system is discussed by a linguistic relation matrix. Finally an example is given to illustrate the proposed method.

References (15)

M. Braae et al.
Theoretical and linguistic aspects of fuzzy logic controller
Automatica
(1979)
Z.Q. Cao et al.
Applicability of some fuzzy implication operators
Fuzzy Sets and Systems
(1989)
J.Q. Chen et al.
Study on stability of fuzzy closed-loop control systems
Fuzzy Sets and Systems
(1993)
J.B. Kiszka et al.
The influence of some fuzzy implication operators on the accuracy of a fuzzy model 1 — Part 1, Part 2
Fuzzy Sets and Systems
(1985)
J.B. Kiszka et al.
The influence of some fuzzy implication operators on the accuracy of a fuzzy model 1 — Part 1, Part 2
Fuzzy Sets and Systems
(1985)
C.C. Lee
Fuzzy logic in control systems: fuzzy logic controller — Part 1
IEEE Trans. Systems Man Cybernet.
(1990)
C.C. Lee
Fuzzy logic in control systems: fuzzy logic controller — Part 2
IEEE Trans. Systems Man Cybernet.
(1990)
M. Sugeno
An introductory survey of fuzzy control
Inform. Sci.
(1985)
R.M. Tong
A control engineering review of fuzzy systems
Automatica
(1977)

There are more references available in the full text version of this article.

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^☆: This project is supported by the National Natural Science Foundation of People's Republic of China.

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Linguistic stability analysis of fuzzy closed loop control systems☆

Abstract

Automatica

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

IEEE Trans. Systems Man Cybernet.

IEEE Trans. Systems Man Cybernet.

Inform. Sci.

Automatica