Discretized Lyapunov-Krasovskii functional method for coupled differential-functional equations with discrete and distributed delays

This article discusses the Lyapunov-Krasovskii functional method for the stability problem of coupled differential-functional equations with distributed delays and one discrete delay. However, systems with distributed delays and multiple commensurate discrete delays can be easily transformed to the standard form treated in this article. This standard form represents a very general class of time-delay systems, which includes as special cases many time-delay systems of retard and neutral type, singular time-delay systems, and some lossless propagation models. Discretization is used to render the stability conditions to an LMI form. Finally, a numerical example is presented to illustrate the effectiveness of the method. Possible extensions are also discussed.