  In Part I, a novel Galerkin-type method for finite dimensional approximations
of transfer functions in Hardy space was developed based on approximation by
simple poles. In Part II, this approximation is applied to system level
synthesis, a recent approach based on a clever reparameterization, to develop a
new technique for optimal control design. To solve system level synthesis
problems, prior work relies on finite impulse response approximations that lead
to deadbeat control, and that can experience infeasibility and increased
suboptimality, especially in systems with large separation of time scales. The
new design method does not result in deadbeat control, is convex and tractable,
always feasible, can incorporate prior knowledge, and works well for systems
with large separation of time scales. Suboptimality bounds with convergence
rate depending on the geometry of the pole selection are provided. An example
demonstrates superior performance of the method.
