Model Reduction of Fuzzy Logic Systems

This paper deals with the problem ofℒ2-ℒ∞model reduction for continuous-time nonlinear uncertain systems. The approach of the construction of a reduced-order model is presented for high-order nonlinear uncertain systems described by the T-S fuzzy systems, which not only approximates the original high-order system well with anℒ2-ℒ∞error performance levelγbut also translates it into a linear lower-dimensional system. Then, the model approximation is converted into a convex optimization problem by using a linearization procedure. Finally, a numerical example is presented to show the effectiveness of the proposed method.