L2−L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology

This paper is concerned with the problem of L2--L∞ synchronization for singularly perturbed complex networks (SPCNs) with semi-Markov jump topology, in which the phenomenon of the singular perturbation is fully taken into consideration. The topology of complex dynamical network is time-varying switching regulated by the semi-Markov jump mechanism. The priority of this work is to obtain some conditions which ensure the underlying complex dynamical network (CDN) is stochastically synchronized with a stated L2--L∞ performance level. Based on Lyapunov method and convex optimization technique, the synchronization conditions can be obtained via solving convex optimization problems. Finally, the correctness and validity of our proposed synchronization method are well demonstrated by a simulation example.