Stability of systems with fast-varying delay using improved Wirtinger's inequality

Abstract

This paper considers the stability of systems with fast-varying delay. The novelty of the paper comes from the consideration of a new integral inequality which is proved to be less conservative than the celebrated Jensen's inequality. Based on this new inequality, a dedicated construction of Lyapunov-Krasovskii functionals is proposed and is showed to have a great potential in practice. The method is also combined with an efficient representation of the improved reciprocally convex combination inequality, recently provided in the literature, in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.