Robust stability criteria for uncertain systems with delay and its derivative varying within intervals

In this paper, stability criteria are proposed for linear systems liable to model uncertainties and with the delay and its derivative varying within intervals. The results are an improvement over previous ones due to the development of a new Lyapunov-Krasovskii functional (LKF). The analysis incorporates recent advances such as convex optimization technique and piecewise analysis method with new delay-interval depedent LKFs terms and a novel auxiliary delayed state. Stability conditions are provided for the cases when the delay derivative is upper and lower bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative. The analysis is enriched with numerical examples that illustrate the effectiveness of our criteria which outperform previous criteria in the literature for nominal and uncertain delayed systems.