Leader-Following Consensus of Multi-agent Systems: New Results Based on a Linear Transformation Approach

This paper investigates the leader-following consensus problem of multiple single-integrators by using a novel linear transformation method together with the input-to-state stability property. The multi-agent system is assumed to contain a single leader, and we consider the following three cases. 1) The leader’s input is pre-given and known by all following agents. 2) The leader’s input is unknown. 3) The leader’s input is measurable online and transmitted to some of follower agents. By constructing a transformation matrix based on incidence matrix of a virtual leader-rooted spanning tree, we make an equivalent transformation from leader-following consensus problem to an input-to-state stability problem. Then we give a necessary and sufficient condition, which is the Hurwitz stability of a matrix associated with the communication topology, for ensuring the leader-following consensus. In order to efficiently check whether the matrix is Hurwitz stable, especially for large-scale multi-agent systems, we further employ the Hurwitz stability criteria of the matrix based on Metzler matrix theory. Finally, we give numerical examples to validate the theoretical results.