Formation tracking of the second-order multi-agent systems using position-only information via impulsive control with input delays

In this paper, the formation tracking problem for the second-order multi-agent system with and without input delay are investigated, respectively. The objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously. The impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay. By using properties of the Laplacian matrix and combining the stability theory of impulsive systems, necessary and sufficient conditions are derived to achieve the formation tracking of the second-order multi-agent system with and without the input delay, respectively. The numerical examples are given to illustrate the effectiveness of our theoretical results.