The effect of membership functions in fuzzy systems on the stability region

Author

El-Arabawy, I.F. ; Rizk, M.R.M. ; Khaddam, H.S.

Author_Institution

Dept. of Electr. Eng., Alexandria Univ., Egypt

Volume

1

fYear

2000

fDate

2000

Firstpage

546

Abstract

The effect of the number of membership functions of the controller´s input variables on the stability boundary of a fuzzy control system is studied. A nonlinear SISO plant in controllable canonical form is considered. The simulation was carried out, first for two membership functions, with different simulation points. It was noticed that inside the indefinite stability region there are some stable states. This means that the estimated stability boundaries were not optimal. It is shown analytically that the number of membership functions has no effect on the stability boundary of the system while the Lyapunov matrix P has an effect. This was justified by the simulation results

Keywords

Lyapunov methods; fuzzy control; nonlinear control systems; stability; Lyapunov matrix; controllable canonical form; fuzzy control system; membership functions; nonlinear SISO plant; simulation points; stability boundaries; stability boundary; stability region; Asymptotic stability; Control systems; Equations; Fuzzy control; Fuzzy sets; Fuzzy systems; Input variables; Nonlinear control systems; Stability analysis; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Electronics, Circuits and Systems, 2000. ICECS 2000. The 7th IEEE International Conference on

Conference_Location

Jounieh

Print_ISBN

0-7803-6542-9

Type

conf

DOI

10.1109/ICECS.2000.911598

Filename

911598