Stability and Stabilization of Polynomial Fuzzy Systems with Time Delay: New Approach

This paper focuses on the stability and stabilization of polynomial fuzzy systems with time delay. This study is based on a polynomial Lyapunov–Krasovskii functional, and delay-dependent results are described in terms of bilinear sum of squares (SOS) conditions. Two techniques are presented, in this paper, to solve the problem of non-convexity of SOS stability and stabilization conditions for polynomial fuzzy systems with time delay. The first technique presents the SOS stability conditions for a specific class of polynomial fuzzy systems with time delay. Delay-dependent conditions are derived throughout a predefined set of indices. This technique improves delay-independent results existing in the literature. The second method transforms the design problem on an optimization problem subject to SOS constraints. The proposed SOS approach is more innovative and effective than the existing linear matrix inequality in terms of conservatism reduction. The new convex conditions for polynomial fuzzy systems with time delay are shown in terms of SOS which can be solved via SOSTOOLS software. Numerical examples are given to show the effectiveness of the proposed methods.