A completely quadratic LKF for coupled differential-functional equations with continuous 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. By means of an equivalent expression of the system, the solution of the original system is obtained by using the fundamental solution. Furthermore, a complete Lyapunov-Krasovskii is obtained, which is necessary and sufficient for the distributed delay system. The functional may be easily extended to deal with the stability problem of uncertain systems with distributed delay via the discretization.