Discretized LKF approach for coupled differential-difference equations with multiple discrete and distributed delays

Time-delay systems described by couple differential-functional equations include as special cases many types of time delay systems and coupled differential-difference systems with time-delays. This article discusses the discretized Lyapunov-Krasovskii functional (LKF) approach for the stability problem of coupled differential-difference equations with multiple discrete and distributed delays. Through independently divided every delay region that the plane regions consists in two delays to discritized the LKF, the stability conditions for coupled systems with multiple discrete and distributed delays are established based on a linear matrix inequality(LMI). The numerical examples show that the analysis limit of delay bound in which the systems is stable may be approached by our result.