H∞ control of uncertain fuzzy continuous-time systems

doi:10.1016/S0165-0114(98)00396-0

Fuzzy Sets and Systems

Volume 115, Issue 2, 16 October 2000, Pages 171-190

https://doi.org/10.1016/S0165-0114(98)00396-0 Get rights and content

Abstract

A new kind of dynamical fuzzy model is proposed to represent the continuous-time complex system which includes both linguistic information and system uncertainties. A new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model. Since the fuzzy model considers the norm-bounded disturbance the controller design problem becomes a $H_{∞}$ control problem. A constructive algorithm is developed to obtain the $H_{∞}$ feedback control law. Finally, an example is given to illustrate the application of the method.

References (18)

S.G. Cao et al.
Identification of dynamic fuzzy systems
Fuzzy Sets and Systems
(1995)
O. Georgieva
Stability of quasilinear fuzzy systems
Fuzzy Sets and Systems
(1995)
H. Nakanishi et al.
A review and comparison of six reasoning methods
Fuzzy Sets and Systems
(1993)
I.R. Petersen
A stabilization algorithm for a class of uncertain linear systems
Systems Control Lett.
(1987)
K. Tanaka et al.
Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
(1992)
H. Ying
Sufficient conditions on general fuzzy systems as function approximators
Automatica
(1994)
J.J. Buckley
Universal fuzzy controllers
Automatica
(1992)
S.G. Cao et al.
Quadratic stability analysis and design of continuous-time fuzzy control system
Internat. J. System Sci.
(1996)
S.G. Cao, N.W. Rees, G. Feng, Analysis and design of uncertain fuzzy control systems, Part I: fuzzy modelling and...

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

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H∞ control of uncertain fuzzy continuous-time systems

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Systems Control Lett.

Fuzzy Sets and Systems

Automatica

Universal fuzzy controllers

Automatica

Quadratic stability analysis and design of continuous-time fuzzy control system

Internat. J. System Sci.

$H_{∞}$ control of uncertain fuzzy continuous-time systems