Improved Stability Method for Linear Time-Varying Delay Systems

In this paper, we consider the stability of the system with time-varying delay. By partitioning the delay interval and taking account of the triple integral term, a new augmented Lyapunov-Krasovskii function (LKF) is proposed. The Wirtinger-based inequality and improved convex combination method are applied to estimate the upper bound of the derivative produced by LKF. For the quadratic functions, we make full use of the convex approaches. The Moon inequality mixes the convex approach is applied to tackle with the integral term made by the Wirtinger-based inequality. Then according to the result, our method can obtain less conservative stability condition. Finally, examples are provided to demonstrate our method is efficiency.