Stability analysis of fuzzy polynomial positive systems with time delay

This paper investigates the stability of fuzzy polynomial positive systems with time delay by using sum-of-squares (SOS) approach. Conservative stability conditions are obtained based on the traditional stability-analysis approach for positive system represented by a fuzzy model, where the membership functions are not considered. In this paper, piecewise-linear membership functions (PLMFs) are employed to relax the stability conditions. Through the PLMFs, the specified non-linearities are able to be considered in the SOS-based stability conditions. The stability analysis result is verified and its effectiveness is demonstrated by a simulation example.