  This paper studies the global feedback stabilization problem of a system with
two pistons and the area between them containing a viscous compressible fluid
(gas) modeled by the Navier-Stokes equations. The control input is the force
applied on the left piston (boundary input) and the overall system consists of
two nonlinear Partial Differential Equations and four nonlinear Ordinary
Differential Equations. Global feedback stabilizers are designed for the
overall system by means of the Control Lyapunov Functional methodology. The
closed-loop system exhibits global asymptotic stability with an exponential
convergence rate. The proposed stabilizing boundary feedback laws do not
require measurement of the density and velocity profiles inside the area
between the pistons and simply require measurements of the gas density and
velocity at the position of the actuated piston.
