Consensus on Directed Matrix-Weighted Networks

Due to the interdependence of multidimensional states between agents in many practical scenarios, it is more accurate to model multiagent systems by matrix coupling networks. However, existing related results rely on undirected networks. In this article, we discuss the consensus problems for matrix-weighted continuous-time, discrete-time multiagent systems over fixed directed network topologies, and switched multiagent 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 multiagent 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 multiagent systems under undirected switching network topology are deduced. At last, some examples are given to demonstrate the correctness of the theoretical results.