Containment control of multi-agent systems with unbounded communication delays

In this paper, we address the containment control problem for multi-agent systems under heterogeneous unbounded communication delays with emphasis on the convergence rate analysis. Different from most works on multi-agent systems, we resort to a viewpoint from the area of positive delay systems. We first cast the containment control problem into the stability analysis of an associated error system. In order to capture the convergence rate, we introduce a nondecreasing positive function whose reciprocal represents the decay rate of the associated error system. Under the assumption that each follower has access to at least one leader and some mild hypotheses on the communication delays, an explicit condition is given to characterise the decay rate of the associated error system in terms of linear programming. In addition, we provide several special cases when the communication delays are restricted by linear, sublinear and logarithmic growth rates, respectively. Finally, through numerical examples, it is shown that the convergence rate is dominated by the delays being the highest order infinitely large quantity.