LMI-based design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno fuzzy model

There have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers. This paper reports on a related study of the Takagi-Sugeno (TS) fuzzy systems, and it is shown that the controller synthesis problems for the nonlinear systems described by the TS fuzzy model can be reduced to convex problems involving linear matrix inequalities (LMIs). After classifying the TS fuzzy systems into three families based on how diverse their input matrices are, a unique controller synthesis procedure is given for each of the families. A numerical example is presented to illustrate the synthesis procedures developed in this paper. (C) 2001 Elsevier Science B.V. All rights reserved.