H∞H∞ synchronization for complex dynamical networks with coupling delays using distributed impulsive control

The H∞H∞ synchronization problem for complex dynamical networks with coupling delays and external disturbance via distributed impulsive control is studied. Two types of time-varying coupling delays are considered: the delays without any restriction on the delay derivatives, and the delays whose derivatives are strictly less than 1. A time-varying Lyapunov function/functional approach is applied to L2L2-gain analysis of the synchronization error systems. H∞H∞ synchronization criteria are established to guarantee the synchronization to be robust with respect to disturbance in the sense that the L2L2-gain from the disturbance to the control output is satisfactorily small. For each type of coupling delays, an algorithm involving convex optimization is proposed to design distributed impulsive controllers achieving a suboptimal value of the sum of coupling strengths for a prescribed L2L2-gain. Two numerical examples illustrate the efficiency of the theoretical results.