Weighted group-consensus analysis of multi-agent systems on a directed bipartite graph

This paper investigates weighted group-consensus problems of multi-agent systems with/without time-delay. Firstly, for the system without time-delay, a decentralized and coordinated controller is designed, and a necessary and sufficient condition is presented, by which weighted group-consensus of multi-agent systems on a directed graph is obtained. Secondly, for the system with time-delay, a upper bound on the maximum time-delay that the system can tolerate is obtained by Nyquist criterion and gerschgorin theorem, and a new control protocol is designed for weighted group-consensus problems of multi-agent system. Finally, two illustrative examples with simulations are studied to support our new results.