Robust stability analysis for systems with time-varying delays: A delay function approach

This paper is concerned with the robust stability of time-varying delay systems with structured uncertainties. Stability conditions are provided through a Lyapunov-Krasovskii functional (LKF) method. The proposed method introduces a linear function of the time-varying delay to construct the LKF. With this function, two-dimensional partition is conducted on the integral domain in the derivative of LKF. Quadratic convex combination then is employed to present stability criteria in the form of linear matrix inequalities (LMIs). The method not only exploits the information of delay at different time instants, but also enables the handling of its derivative to reduce conservatism. Numerical examples are given to show the effectiveness of our method.