Leader

This paper considers the leader-following consensus problem for nonlinear multiagent systems with large delays. The time delays switch alternately between two different kinds of delays, called a small delay and a large delay. New Lyapunov functionals that depend on graph information are constructed. To guarantee the desired leader-following consensus, the concepts of the length and frequency of the large delay periods are introduced. Sufficient conditions for consensus are given in terms of linear matrix inequalities. Furthermore, low-dimensional criteria that are easily implemented especially for large-scale multiagent systems are provided. Finally, two simulation examples are presented to validate the effectiveness of the proposed scheme