Distributed Synchronization of Complex Dynamical Networks Using Delayed Impulsive Control

The robustness of the distributed impulsive synchronization scheme with regards to impulse transmission delays is studied. Suppose that a distributed impulsive controllers for a class of complex dynamic networks is impacted by transmission delays. An impulse-time-dependent Lyapunov function is presented to analyze the stability of the synchronization error dynamics. Through integrating the Razumikhin-type technique, Newton-Leibniz formula, and convex combination method, a robust distributed impulsive synchronization criterion is derived. In addition, an algorithm is proposed to design a distributed impulsive control gain matrix to attain the suboptimal value of the minimum sum of coupling strengths. The beneficial effect of the current distributed synchronization approach is confirmed by numerical simulations.