Stabilization of Uncertain Linear System with Time-varying Delay Using a New Lyapunov-Krasovskii Functional

Abstract

This paper presents a static state feedback controller design for uncertain linear systems with varying time delay. A less conservative stability criterion is derived invoking a new Lyapunov-Krasovskii (LK) functional. The reciprocally convex combination lemma and Wirtinger’s inequality are exploited to develop a computationally tractable method where the design constraints are formulated in linear matrix inequality (LMI) framework. Numerical examples are given to demonstrate the superiority of the proposed results over the existing methods.