  Various new implicit parameterizations for stabilizing controllers that allow
one to impose structural constraints on the controller have been proposed
lately. They are convex but infinite-dimensional, formulated in the frequency
domain with no available efficient methods for computation. In this paper, we
introduce a kernel version of the Youla parameterization to characterize the
set of stabilizing controllers. It features a single affine constraint, which
allows us to recast the controller parameterization as a novel robust filtering
problem. This makes it possible to derive the first efficient Linear Matrix
Inequality (LMI) implicit parametrization of stabilizing controllers. Our LMI
characterization not only admits efficient numerical computation, but also
guarantees a full-order stabilizing dynamical controller that is efficient for
practical deployment. Numerical experiments demonstrate that our LMI can be
orders of magnitude faster to solve than the existing closed-loop
parameterizations.
