Title: Localized and Distributed H2 State Feedback Control

Abstract: Distributed linear control plays a crucial role in large-scale cyber-physical systems. It is generally desirable to both impose information exchange (communication) constraints on the distributed controller, and to limit the propagation of disturbances to a local region without cascading to the global network (localization). Recently proposed System Level Synthesis (SLS) theory provides a framework where such communication and localization requirements can be tractably incorporated in controller design and implementation. In this work, we develop upon the SLS framework and derive a solution to the localized and distributed H2 state feedback control problem, which previously could only be solved via the FIR (Finite Impulse Response) approximation. In particular, the proposed synthesis procedure can be decomposed column-wise, and is therefore scalable to arbitrary large-scale networks. Further, we lift the FIR filter requirement for SLS controllers and make explicit the distributed and localized state space implementation of the controller in the infinite-horizon case. Our simulation demonstrates superior performance and numerical stability of the proposed procedure over previous methods.