Decomposition property of fuzzy systems and its applications

Author

Zeng, Xiao-Jun ; Singh, Madan G.

Author_Institution

Dept. of Comput., Univ. of Manchester Inst. of Sci. & Technol., UK

Volume

4

Issue

2

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

149

Lastpage

165

Abstract

This paper presents the decomposition property of fuzzy systems using a simple, constructive, decomposition procedure. That is, by properly dividing the input space into sub-input spaces, a general fuzzy system is decomposed into several sub-fuzzy systems which are the simplest fuzzy systems in the sub-input spaces. Based on the decomposition property of fuzzy systems, the analysis of fuzzy systems can be divided into two steps: first, analyze the properties of the simplest fuzzy systems, and then, use the decomposition property to extend the results to general fuzzy systems. Using this idea, two applications of the decomposition property are given. The first is the application to the representation capability analysis of fuzzy systems. The second is the application to the analysis of a class of nonlinear control systems. Then, based on the piecewise affine fuzzy-system model, the existence condition and the design of a stable control for a class of single-input single-output (SISO) nonlinear systems are presented

Keywords

asymptotic stability; closed loop systems; fuzzy control; fuzzy set theory; fuzzy systems; inference mechanisms; intelligent control; nonlinear systems; SISO nonlinear systems; asymptotic stability; closed loop systems; decomposition; fuzzy rule base; fuzzy set theory; fuzzy systems; inference engines; principal components; stable control; sub-input spaces; Control systems; Control theory; Fuzzy systems; Intelligent control; Mathematical model; Nonlinear control systems; Nonlinear systems; Piecewise linear approximation; Piecewise linear techniques; Systems engineering and theory;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.493909

Filename

493909