Refined stability of a class of CDFE with distributed delays

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. In order to eliminate the influence of discontinuities which are from the distributed delay, a simple LKF is attached to the complete quadratic LKF as a complementary to improve solution of the result presented by linear matrix inequalities(LMIs). Discretization is used to render the stability conditions of the LMI form for the whole systems, where those discontinuous points are regarded as some partition of divided points in the discretized process. 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 are presented to illustrate the superiority of the method.