  The recently introduced structured input-output analysis is a powerful method
for capturing nonlinear phenomena associated with incompressible flows, and
this paper extends that method to the compressible regime. The proposed method
relies upon a reformulation of the compressible Navier-Stokes equations, which
allows for an exact quadratic formulation of the dynamics of perturbations
about a steady base flow. To facilitate the structured input-output analysis, a
pseudo-linear model for the quadratic nonlinearity is proposed and the
structural information of the nonlinearity is embedded into a structured
uncertainty comprising unknown `perturbations'. The structured singular value
framework is employed to compute the input-output gain, which provides an
estimate of the robust stability margin of the flow perturbations, as well as
the forcing and response modes that are consistent with the nonlinearity
structure. The analysis is then carried out on a plane, laminar compressible
Couette flow over a range of Mach numbers. The structured input-output gains
identify an instability mechanism, characterized by a spanwise elongated
structure in the streamwise-spanwise wavenumber space at a subsonic Mach
number, that evolves into an oblique structure at sonic and supersonic Mach
numbers. In addition, the structured input-output forcing and response modes
provide insight into the thermodynamic and momentum characteristics associated
with a source of instability. Comparisons with a resolvent/unstructured
analysis reveal discrepancies in the distribution of input-output gains over
the wavenumber space as well as in the modal behavior of an instability, thus
highlighting the strong correlation between the structural information of the
nonlinearity and the underlying flow physics.
