New stability criteria for linear time-delay systems using complete LKF method

This paper focuses on the stability test for linear systems with time-varying delay and provides new stability conditions in terms of linear matrix inequalities (LMIs). The basic idea is the use of complete Lyapunov–Krasovskii functional (LKF) method and the derivation employs the discretisation technique and the reciprocally convex combination. The main feature of this work lies in that the present result not only leads to some improvements over existing results in the LMI framework but also is applicable for time-delay systems with unstable delay-free case. Three numerical examples are given to show the effectiveness and merits of the present result.