Stability analysis and stabilisation of delayed IT2 fuzzy systems based on the Bessel–Legendre inequality

Abstract

This study is concerned with the problems of asymptotic stability analysis and stabilisation for interval type-2 (IT2) fuzzy systems with time-varying delays. An augmented Lyapunov–Krasovskii functional including triple-integral terms is constructed. By the second-order Bessel–Legendre integral inequality and the reciprocally convex combination, a good estimation of the derivative for the Lyapunov–Krasovskii functional can be derived. Thus, sufficient asymptotic stability conditions for the delayed IT2 fuzzy system are established. The proposed method provides improvements and produces better results than the existing ones in the literature. Furthermore, in light of Finsler's lemma and the obtained asymptotic stability conditions, a state feedback controller for the delayed IT2 fuzzy system is developed. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.