Dynamic boundary stabilization of linear and quasilinear hyperbolic systems

Abstract — Systems governed by hyperbolic partial differential equations with dynamics associated with their boundary con-ditions are considered in this paper. These infinite dimensional systems can be described by linear or quasi-linear hyperbolic equations. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of such systems. A polytopic approach is developed for quasi-linear hyperbolic systems in order to guarantee stability in a region of attraction around an equilibrium point, given specific bounds on the parameters. The main results are illustrated on the model of an isentropic inviscid flow. I