Stability analysis of polynomial fuzzy systems with time-delay via sum of squares (SOS) approach

This paper presents a sum of squares (SOS) approach to stability analysis of polynomial fuzzy systems with time-delay. Based on a novel polynomial Lyapunov-Krasovskii Functional, stability conditions are presented in terms of sum of squares in order to reduce the conservatism. The proposed SOS-based framework is more innovative and effective than the existing linear matrix inequality (LMI). The SOS designed conditions can be solved via the recent developed toolbox of Matlab, SOSTOOLS V3.00. Numerical example is given to illustrate the utility of the proposed approach.