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Discretized LKF approach for stability of a class of coupled differential-difference equations with multiple known and unknown delays

This article discusses the discretized Lyapunov-Krasovskii functional (LKF) approach for the stability problem of a class of coupled differential-difference equations with multiple discrete and distributed delays. Through independently divided every known delay region that the plane regions consists in two known delays to discritized the LKF, the stability conditions for coupled systems with multiple known and unknown discrete delays and known distributed delays are established based on a linear matrix inequality (LMI), which is dependent with the known or small time-delays, is independent with those unknown or large time-delays. Finally, The numerical examples illustrate that the result is reliable and effective.