Average consensus in networks of dynamic multi-agents with switching topology: Infinite matrix products

This paper deals with the average consensus problem in a multi-agent system with switching interaction topology modeled as a weighted digraph. The convergence analysis is performed in both discrete-time and continuous-time dynamics based on the theory of infinite matrix products. Conditions for system convergence to average consensus are derived in the form of constraints on direct and reverse graphs and the structure of adjacency elements among the agents. Furthermore, a sufficient condition is provided for convergence to average consensus in systems in which the interaction topology is balanced over infinite contiguous non-overlapping time intervals instead of being balanced continuously. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.