Chapter 7 Fuzzy Combined Controller for Nonlinear Systems

Abstract

Lyapunov approach is the most common approach to investigate the system stability of fuzzy control systems based on the TS fuzzy model. The stability of the FMB control systems with imperfectly/perfectly matched premise membership functions are reviewed in Chapter 2. In general, the stability conditions for the FMB based control systems with perfectly matched premise membership functions are more relaxed. However, it is required that the TS fuzzy model in the form of (2.2) is uncertainty free. As discussed in Chapter 2, the fuzzy controller (2.6) demonstrates an inherent robustness property on dealing with nonlinear plant subject to a certain level of parameter uncertainties by presenting the parameter uncertainties to the membership functions of the fuzzy model. To deal with the parameter uncertainties, in this chapter, a TS fuzzy model subject to parameter uncertainties is proposed for doing the stability analysis. Stability conditions for this class of nonlinear systems were investigated in [74, 104].