Overcoming the Fixed-Spectrum Obstacle in Decentralized Control.

It is well known that the "fixed spectrum" of a jointly controllable, jointly observable, multi-channel linear system is an obstacle to its stabilization with decentralized control. In this paper, it is constructively shown that a system's fixed spectrum is not in fact an obstacle to its stabilization, provided that distributed control with message passing is used and that the graph of the network on which the system is defined is strongly connected. This is true for both continuous-time and discrete-time systems. Moreover, these observations still hold if transmission delays are present on the network, at least for discrete-time systems.