  In this article, we study the linear time-invariant state-feedback controller
design problem for distributed systems. We follow the recently developed system
level synthesis (SLS) approach and impose locality structure on the resulting
closed-loop mappings; the corresponding controller implementation inherits this
prescribed structure. In contrast to existing SLS results, we derive an
explicit (rather than implicit) parameterization of all achievable stabilized
closed-loops. This admits more efficient IIR representations of the temporal
part of the closed-loop dynamics, and it allows for the H2 design problem with
closed-loop spatial sparsity constraints to be converted to a standard model
matching problem, with the number of transfer function parameters scaling
linearly with the closed-loop spatial extent constraint. We illustrate our
results with two applications: consensus of first-order subsystems and the
vehicular platoons problem. In the case of first-order consensus, we provide
analytic solutions and further analyze the architecture of the resulting
controller implementation. Results for infinite extent spatially invariant
systems are presented to provide insight to the case of a large but finite
number of subsystems.
