Distributed control of linear time-varying systems interconnected over arbitrary graphs

In this paper, we focus on designing distributed controllers for interconnected systems in situations where the controller sensing and actuation topology is inherited from that of the plant. The distributed systems considered are composed of discrete-time linear time-varying subsystems interconnected over arbitrary graph structures. The main contribution of this paper is to provide results on general graph interconnection structures in which the graphs have potentially an infinite number of vertices. This is accomplished by first extending previous machinery developed for systems with spatial dynamics on the lattice Zn. We derive convex analysis and synthesis conditions for design in this setting. These conditions reduce to finite sequences of LMIs in the case of eventually periodic subsystems interconnected over finite graphs. The paper also provides results on distributed systems with communication latency and gives an illustrative example on the distributed control of hovercrafts along eventually periodic trajectories. The methodology developed here provides a unifying viewpoint for our previous and related work on distributed control.