Improved stabilization criteria for Takagi–Sugeno fuzzy systems with variable delays

• A new integral inequality is proposed to estimate the quadratic integral terms. • A new and augmented LKF is constructed by using the concept of delay-partitioning techniques. • An improved stability and stabilization condition for T–S fuzzy systems with delays is obtained. • Three numerical examples are presented to show the efficacy of the proposed results. In the present research, the stability analysis and stabilization of nonlinear processes characterized by the Takagi–Sugeno (T–S) fuzzy model with variable time delays have been investigated. The state’s delay is presumed to belong to a given interval, ensuring that the delay lower limit is not constrained to zero. First, a new and improved integral inequality (II) lemma is proposed to deal with the cross-product terms in the derivative of the constructed delay-product-type (DPT) augmented Lyapunov–Krasovskii functional (LKF). Second, a novel delay-range-dependent (DRD) stability condition and parallel distributed compensation (PDC) technique-based stabilization condition is then achieved in terms of linear matrix inequalities (LMIs). Finally, to illustrate the superiority of the proposed stability criterion and controller design approach over existing ones, three numerical examples are given.