A novel integral inequality and its application to stability analysis of linear system with multiple time delays

Abstract

The integral inequality plays a key role in developing delay-dependent stability criteria for the linear system with multiple time delays. This paper investigates a novel integral inequality to bound the integral terms in the derivative of the Lyapunov–Krasovskii functional (LKF). Compared with the auxiliary function-based integral inequality, the presented integral inequality is more general. By removing the involved auxiliary function, the integral term in the bound is linearly represented with a sequence of integrals only related to the system state. After a newly augmented LKF is constructed with multiple integral terms concerning the relationships among multiple delays, an adjustable and relaxed stability criterion is established in terms of linear matrix inequalities using the proposed inequality. Two numerical examples are given to show the merits of the proposed method.