Position convergence of informed agents in flocking problem with general linear dynamic agents

In most existing works on the flocking problem, results were obtained for the case where a double integrator dynamic is used to describe motion of agents and virtual leader. These results, however, may not be generalised to agents with general linear dynamic. In this study, it is shown that in the flocking of agents with a linear dynamic, the velocity convergence of agents does not generally lead to the position convergence of informed agents and the position convergence is possible only for a specified group of linear dynamics. In this study, a control protocol is proposed to flock agents with specified linear dynamics and guarantee the velocity convergence of all agents as well as average position convergence of informed agents to those of the virtual leader.