Optimal realizable networked controllers for networked systems

In this paper, we provide the optimal solution for the H₂ control problem in the case when both plant and controller are interconnected systems interacting over an arbitrary directed causal network. We first analyze the structure of network realizable systems and then characterize the set of all stabilizing controllers that are realizable over the given network using the Youla parametrization. The H₂ control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given network. The results of this paper allow one to apply many classical results and approaches of multi-variable robust control to networked systems.