  We present a simple and effective way to account for non-convex costs and
constraints~in~state feedback synthesis, and an interpretation for the
variables in which state feedback synthesis is typically convex. We achieve
this by deriving the controller design using moment matrices of state and
input. It turns out that this approach allows the consideration of non-convex
constraints by relaxing them as expectation constraints, and that the variables
in which state feedback synthesis is typically convexified can be identified
with blocks of these moment matrices.
