A survey on Lyapunov-based methods for stability of linear time-delay systems

Recently, stability analysis of time-delay systems has received much attention. Rich results have been obtained on this topic using various approaches and techniques. Most of those results are based on Lyapunov stability theories. The purpose of this article is to give a broad overview of stability of linear time-delay systems with emphasis on the more recent progress. Methods and techniques for the choice of an appropriate Lyapunov functional and the estimation of the derivative of the Lyapunov functional are reported in this article, and special attention is paid to reduce the conservatism of stability conditions using as few as possible decision variables. Several future research directions on this topic are also discussed.