Dynamic Boundary Stabilization of Linear Parameter Varying Hyperbolic Systems: Application to a Poiseuille Flow

The problem of boundary control in first order linear parameter varying (LPV) hyperbolic systems with dynamics associated with the boundary conditions is considered in this article. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of these infinite dimensional systems. A polytopic approach is developed in order to synthesize a robust boundary control which guarantees the exponential stability for a given convex parameter set. An application using a Poiseuille flow control experimental setup illustrates the main results.