Contents I. Introduction
Control of nonlinear systems is difficult because we do not have systematic mathematical tools to help finding a necessary and sufficient condition to guarantee the stability and performance. The problem will become more complex if some of the parameters of the plant are unknown. By using a TSK fuzzy plant model [1]–[2], [7], [14] a nonlinear system can be expressed as a weighted sum of some simple sub-systems. This model gives a fixed structure to some of the nonlinear systems and thus facilitates the analysis of the systems. There are two ways to obtain the fuzzy plant model: 1) by performing system identification methods based on the input-output data of the plant [1]–[2], [7], [14], 2) deriving from the mathematical model of the nonlinear plant [5]. Stability of fuzzy model based systems has been investigated recently [4], [6]–[13]. A linear controller [13] was also proposed to control the plant. Most of the fuzzy controllers proposed are functions of the grades of membership of the fuzzy plant model. Hence, the membership functions of the fuzzy plant model must be known. It means that the parameters of the nonlinear plant must be known or be constant when the identification method is used to derive the fuzzy plant model. Practically, the parameters of many nonlinear plants will change during the operation, e.g., the load of a dc-dc converter, the number of passengers on board a train. In these cases, the robustness property of the fuzzy controller is an important concern.
