Impulsive synchronization for uncertain delayed complex dynamical networks with minimal coupling strength

This paper investigates the impulsive synchronization problem of complex dynamical network system (CDNs) with uncertainty and coupling time-varying delay. The aim is to design distributed impulsive controllers with minimum necessary coupling strength. A time-varying Lyapunov function based method is proposed to find the synchronization condition for the impulsively controlled CDNs. By utilizing a convex combination technique, the derived synchronization condition is expressed in terms of linear matrix inequalities (LMIs). Then, an optimization algorithm is proposed to design the distributed impulsive controller with minimum coupling strength. Finally, an example is presented to illustrate the effectiveness of the theoretical results.