Localized distributed state feedback control with communication delays

This paper introduces the notion of localizable distributed systems. These are systems for which a distributed controller exists that limits the effect of each disturbance to some local subset of the entire plant, akin to spatio-temporal dead-beat control. We characterize distributed systems for which a localizing state-feedback controller exists in terms of the feasibility of a set of linear equations. We then show that when a feasible solution exists, it can be found in a distributed way, and used for the localized synthesis and implementation of controllers that lead to the desired closed loop response. In particular, by allowing controllers to exchange both state and control actions, the information needed by a particular controller is limited to a local subset of the system's state and control inputs