A convex characterization of distributed control problems in spatially invariant systems with communication constraints

In this paper we consider the problem of distributed controller design in spatially invariant systems for which communication among sites is limited. In particular, the controller is constrained so that information is propagated with a delay that depends on the distance between subsystems-a structure we refer to as “funnel” causality. We show that the problem of optimal design can be cast as a convex problem provided that the plant has a similar funnel-causality structure, and the propagation speeds in the controller are at least as fast as those in the plant. As an example, we consider the case of the wave dynamics with limited propagation speed control.