Leader-following consensus of multi-agent systems with and without time-delay

In this paper, we discuss the consensus problems of a multi-agent system with and without time-delay. The multi-agent system was considered with an active leader and a group of autonomous agents. To track the active leader, a neighbor-based local control law and a neighbor-based state-estimation rule for each autonomous agent were proposed by a recent reference, which proved the multi-agent system can reach consensus with assumption that a positive weighted parameter is less than 1. By constructing a parameter-dependent Lyapunov function, we proved that the multi-agent system can also reach consensus for the given weighted parameter is equal or greater than 1 with and without time-delay. Finally, a numerical example is given to illustrate the obtained results.