Synchronization of a linear singularly perturbed complex network with potential application in electric power systems

This paper is concerned with the synchronization problem for a linear singularly perturbed complex network. The slow sub-network and the fast subnetwork are obtained on the different time-scale by employing singularly perturbed decomposition method. Sufficient conditions for the synchronization of the two sub-networks are obtained by introducing the reference error system and analyzing the corresponding stability. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities that can be easily solved by using semi-definite programming method. A practical model concerning an electric system grid with N synchronous machines is established, which can be used to illustrate the potential applicability of the proposed results.