Consensus on Directed Matrix-Weighted Networks

Abstract

Due to the interdependence of multi-dimensional states between agents in many practical scenarios, it is more accurate to model multi-agent systems by matrix coupling networks. However, existing related results rely on undirected networks. This paper discusses the consensus problems for matrix-weighted continuous-time, discrete-time multi-agent systems over fixed directed network topologies, and switched multi-agent systems switching between continuous-time dynamics and discrete-time dynamics over fixed directed and switching undirected network topologies. Under the proposed matrix-weighted algorithms, for continuous-time, discrete-time and switched multi-agent systems, the consensus criteria are established over fixed directed network topologies by analysis theory and matrix theory. Besides, using Lyapunov stability theory, the consensus conditions of switched multi-agent systems under undirected switching network topology are deduced. At last, some examples are given to demonstrate the correctness of the theoretical results.