ABSTRACT
T-S fuzzy models described in the previous chapters are assumed to be accurate in describing the underlying systems. However, in practice, many complex nonlinear dynamic systems are subject to varieties of uncertainties such as parameter uncertainties or even structure variations. Quite often these uncertainties degrade the performance of the resulting closed-loop control systems, or even worse, lead to instability if they are not dealt with adequately in the controller design process. In this chapter, a class of uncertain T-S fuzzy systems is introduced, and the issue of their stabilization and H∞controller synthesis is addressed based on piecewise and fuzzy quadratic Lyapunov functions, respectively. It is also noted that the common quadratic Lyapunov functions are special cases of piecewise and fuzzy quadratic Lyapunov functions and thus the corresponding results based on common quadratic Lyapunov functions are presented as corollaries.
