Stability and stabilization of T–S fuzzy systems with variable delays via new Bessel–Legendre polynomial based relaxed integral inequality

Abstract

This paper investigates the delay-range-dependent (DRD) stability problem in regards to continuous time Takagi–Sugeno (T–S) fuzzy system with variable delays. First, a new integral inequality Lemma referred herein as higher order polynomial based relaxed integral inequality (HOPBRII) is proposed to reduce the estimation gap of the current work with that of Bessel–Legendre polynomial based inequality (BLPBI). Next, a suitable Lyapunov–Krasovskii functional (LKF) is constructed with delay product terms and then using the proposed inequality, suitable condition for DRD stability and stabilization condition of the considered T–S fuzzy system are derived in a linear matrix inequality (LMI) framework. To analyse the advantage theoretically and less conservatism of the proposed method, a new DRD stability condition using similar LKFs and the BLPBI approach is further derived herein. Finally, the efficacy of the proposed stability and stabilization conditions are validated through the solutions of four numerical examples.