Ho. Wang et al., AN APPROACH TO FUZZY CONTROL OF NONLINEAR-SYSTEMS - STABILITY AND DESIGN ISSUES, IEEE transactions on fuzzy systems, 4(1), 1996, pp. 14-23
We present a design methodology for stabilization of a class of nonlin
ear systems. First, we represent a nonlinear plant with a Takagi-Sugen
o fuzzy model. Then a model-based fuzzy controller design utilizing th
e concept of the so-called ''parallel distributed compensation'' is em
ployed. The main idea of the controller design is to derive each contr
ol rule so as to compensate each rule of a fuzzy system. The design pr
ocedure is conceptually simple and natural. Moreover, the stability an
alysis and control design problems can be reduced to linear matrix ine
quality (LMI) problems. Therefore, they can be solved efficiently in p
ractice by convex programming techniques for LMI's. The design methodo
logy is illustrated by application to the problem of balancing and swi
ng-up of an inverted pendulum on a cart.