Controllability is not sufficient for pole placement in patterned systems

In distributed systems, a common question is how to synthesize a control law that adheres to the system's distributed interconnection structure. One promising synthesis approach involves encoding the system's interconnections as a pattern in the system matrices, and carrying this pattern through all steps of a control design. To date, though, all control results on this front have had limitations on which distributed structures are admissible. In this paper, we provide a pole placement result that is valid for more general system patterns. We also show that a system's controllability does not imply patterned pole placement, so we introduce a novel notion of controllability for patterned distributed systems.