Polyhedral cone invariance applied to rendezvous of multiple agents

In this paper, we pose the N-scalar agent rendezvous as a polyhedral cone invariance problem in the N dimensional phase space. The underlying dynamics of the agents are assumed to be linear. We derive a condition for positive invariance for polyhedral cones. Based on this condition, we demonstrate that the problem of determining a certificate for rendezvous can be stated as a convex feasibility problem. Under certain rendezvous requirements, we show that there are no robust closed-loop linear solutions that satisfy the invariance conditions. We show that the treatment of the rendezvous problem on the phase plane can be extended to the case where agent dynamics are non-scalar.