The Price of Distributed Design in Optimal Control

We study control design strategies which, when presented with a plant made of interconnected subsystems, construct a sub-controller for each one of them using only a model of this particular subsystem. We prove that, for a class of linear time-invariant, discrete-time systems, any such distributed control strategy must have a worst-case performance at least twice the optimal. The best distributed design strategy is one that results in a deadbeat controller for every plant.