Synchronization in Networks of Linear Systems With Three Time Scales

In this paper, we study the synchronization for networks with three-time-scale linear systems. This article uses a fixed undirected graph to describe the topology of the network. Under mild assumptions, we perform a two-stage reduction on the singularly perturbed systems and get approximate systems. The analysis of the reduced systems shows the form of the state feedback controller that implements the asymptotic synchronization of the approximation system. The synchronization of the network is changed into achieve simultaneous stabilization of state using variable transformation. According to the reduced approximate system's relevance to the original singularly perturbed system, we design the state feedback controller which can achieve the asymptotic synchronization of the original networks. Our results are illustrated by a numerical examples.