Consensus Problem of Leader-following Second-order Multi-agent Systems with Time-delay under Directed Topology

In this paper, consensus problems of a kind of continuous-time second-order MAS with communication delays is studied. A neighbor-based linear consensus protocol with time delay is introduced based on the fixed communication topology firstly, and then a necessary and sufficient condition for the system is derived based on graph theory and quadratic stability theory. An equality is proposed for obtaining the maximum time delay which is induced in the positions and velocities. Numerical simulations are carried out to further illustrate the effectiveness of the proposed theoretical results.