Robust Stability Analysis of Time-varying Delay Systems via an Augmented States Approach

This paper focuses on the robust stability analysis of linear systems with time varying delays. The second derivative of the state is used to construct a novel Lyapunov-Krasovskii functional (LKF). Then, both the integrals and derivatives of the states along with the delayed states could be taken into consideration in handling of the LKF. We introduce these augmented variables and establish correlations between them. Moreover, our approach makes it available that quadratic convex combination can be applied not only to the time delay, but also to the derivative of it. Robust stability criteria are presented, and numerical examples illustrate that the methods are less conservative.