$ {\cal H}_{2}$-Optimal Decentralized Control Over Posets: A State-Space Solution for State-Feedback

We develop a complete state-space solution to H
₂
-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is an intuitive description of the controller as an aggregation of local control laws.