Global Stabilization of Compressible Flow between Two Moving Pistons

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