Stability of coupled differential-functional equations with discrete and distributed delays via discretized LKF method

This article discusses the Lyapunov-Krasovskii functional (LKF) method for the stability problem of coupled differential-functional equations with distributed delays and one discrete delay. Discretization is used to render the stability conditions of an LMI form for the systems. The conclusion may be easily extended to deal with the stability problem of systems with either distributed delays and multiple commensurate discrete delays or mix delays. Finally, the numerical examples is presented to illustrate the effectiveness of the method.