  We study stability and input-state analysis of three dimensional (3D)
incompressible, viscous flows with invariance in one direction. By taking
advantage of this invariance property, we propose a class of Lyapunov and
storage functionals. We then consider exponential stability, induced L2-norms,
and input-to-state stability (ISS). For streamwise constant flows, we formulate
conditions based on matrix inequalities. We show that in the case of polynomial
laminar flow profiles the matrix inequalities can be checked via convex
optimization. The proposed method is illustrated by an example of rotating
Couette flow.
