An Explicit State-Space Solution for a Decentralized Two-Player Optimal Linear-Quadratic Regulator

We develop controller synthesis algorithms for decentralized control problems, where individual subsystems are connected over a network. We focus on the simplest information structure, consisting of two interconnected linear systems, and construct the optimal controller subject to a decentralization constraint via a spectral factorization approach. We provide explicit state-space formulae for the optimal controller, characterize its order, and show that its states are those of a particular optimal estimator.