Coordination control for generic linear multi-agent systems with time delay: A semi-discretization approach

This paper aims to perform the convergence analysis for a group of linear multi-agent systems with time delay and communicating over arbitrary network topology. It is proved that within the allowable delay bound, all the agents within each closed strong component reach synchronization, while all the other agents outside the closed strong components converge to the dynamic convex hull spanned by the agents in the closed strong components. The delay bound is calculated by the method of semi-discretization, which is also useful in searching for an optimal feedback control with the fastest convergence rate for a certain time delay. A simulation example is given to illustrate the validity of the obtained results.