Stabilization via Distributed Control

We consider the linear plant with multiple pairs of input and output channels, and solve the problem of designing a stabilizing controller consisting of a set of control stations, one for each channel pair, connected with an arbitrarily fixed network topology and communication dynamics. It is shown that such stabilizing distributed controller exists if and only if the fixed modes of the plant, augmented with the network communication, are stable; this leverages and extends the classical fixed mode result for decentralized control. Moreover, a condition is given to reveal exactly what connections are needed between control stations to achieve stabilizability via a distributed control. Thus, the feasibility of optimal distributed control synthesis can readily be checked or enforced before applying computationally expensive optimization methods. Stabilizing distributed controllers, if feasible, can be designed using decentralized control theories.