Consensus and Products of Substochastic Matrices: Convergence Rate With Communication Delays

This study analyzes the convergence rate of leader–follower multiagent consensus under communication delays by developing a measure standard utilizing products of substochastic matrices. Through the construction of augmented auxiliary digraphs, which combine the binary relations composition, a comprehensive analysis of the leader–follower consensus dynamics is conducted. A mathematical representation of the least convergence rate of the system is established, which is closely related to the network structure, the upper bound of weight factors as well as the size of time delays. Moreover, an upper bound on the finite convergence time of the system with special topological structures, such as chain graph, star graph, and tree graph is given. At last, simulated examples are presented to confirm the theoretical findings.