Discretized LKF method for stability of coupled differential‐difference equations with multiple discrete and distributed delays

Time‐delay systems described by coupled 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) method for the stability problem of coupled differential‐difference equations with multiple discrete and distributed delays. Through independently dividing every delay region that the plane regions consists in two delays to discretize LKF, the exponential 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 are stable may be approached by our result. Copyright © 2011 John Wiley & Sons, Ltd.