Stability analysis and stabilization of polynomial fuzzy systems with time-delay via a Sum Of Squares (SOS) approach

This paper is concerned with stability analysis and stabilization of polynomial fuzzy systems with a varying time delay. Based on a novel polynomial Lyapunov-Krasovskii Functional, the less conservatism delay dependent results are presented in terms of Sum Of Squares (SOS) which improve previous works. The proposed SOS-based framework is more innovative and effective than the existing Linear Matrix Inequality (LMI) based approaches. The SOS designed conditions are solved using SOSTOOLS toolbox. The validity and applicability of the proposed approach is shown by a numerical example.