Multiagent Systems on Multilayer Networks: Synchronization Analysis and Network Design

This paper is concerned with the synchronization of multiagent systems connected via different types of interactions, known as multilayer networks. Additive coupling and Markovian switching coupling are proposed to capture the layered connections with two kinds of mathematical models constructed. First, based on simultaneously diagonalization of multiple Laplacian matrices, a general criterion is derived, ensuring that the synchronization problem with additive coupling can be decoupled. Then, an alternative condition is presented, which is related to the number of layers, regardless of the number of agents. With the derived criteria, a concept of joint synchronization region is introduced and further discussed as a network design problem. Synchronization with Markovian switching layers is also analyzed in parallel, exemplified by some special cases of two-layer networks. Finally, a group of cellular neural networks coupled by two-layer connections are chosen to illustrate the effectiveness of the theoretical results.