  This paper proposes a novel input-output parametrization of the set of
internally stabilizing output-feedback controllers for linear time-invariant
(LTI) systems. Our underlying idea is to directly treat the closed-loop
transfer matrices from disturbances to input and output signals as design
parameters and exploit their affine relationships. This input-output
perspective is particularly effective when a doubly-coprime factorization is
difficult to compute, or an initial stabilizing controller is challenging to
find; most previous work requires one of these pre-computation steps. Instead,
our approach can bypass such pre-computations, in the sense that a stabilizing
controller is computed by directly solving a linear program (LP). Furthermore,
we show that the proposed input-output parametrization allows for computing
norm-optimal controllers subject to quadratically invariant (QI) constraints
using convex programming.
