A Novel Generalized Integral Inequality Based on Free Matrices for Stability Analysis of Time-Varying Delay Systems

This paper proposes a novel generalized integral inequality based on free matrices and applies it to stability analysis of time-varying delay systems. The proposed integral inequality estimates the upper bound of the augmented quadratic term of the state and its derivative term by utilizing not only the single integral term but also the higher-order multiple integral terms. The proposed integral inequality includes several well-known integral inequalities as special cases. For the stability analysis of time-varying delay systems, a new Lyapunov-Krasovskii functional is constructed by including the double integral term with the augmented vector of the state and its derivative to utilize the proposed integral inequality when estimating the derivative of the Lyapunov-Krasovskii functional. Furthermore, to fully exploit the information on the time-varying delay, this paper divides the interval of the double integral term into two parts. Two numerical examples show that the results of the proposed method outperform those of the existing methods.