Stability analysis of systems with time-varying delay via a delay-product-type integral inequality

This paper is concerned with the issue of stability analysis of systems with time-varying delay. First, a delay-product-type (DPT) integral inequality is proposed, which combines the third-order Bessel-Legendre (TOBL) integral inequality and the reciprocally convex (RC) inequality into a unified integral inequality; then, a tight upper bound on the time-derivative of the Lyapunov-Krasovskii functional (LKF) can be obtained. Second, an augmented LKF is tailored for the use of the DPT integral inequality; then, more information about the instant state and the delayed states is taken into account. Third, by using the DPT integral inequality and the augmented LKF, some less conservative conditions that ensure the stability of systems with time-varying delay are derived. Finally, simulations are provided to illustrate the advantage of our proposed method.