Boundary feedback stabilization of a linearized compressible adiabatic flow through a porous media by backstepping method

This paper investigates the boundary feedback stabilization of the one-dimensional linearized hyperbolic system (LHS), which models compressible adiabatic flow through porous media. The backstepping method was applied to control the LHS through Dirichlet boundary control. In this context, we proved that the solution of the LHS is exponentially stable under the effect of a designed Dirichlet feedback control law. Furthermore, the exponential decay rate depends solely on the parameters of the LHS. Finally, some numerical experiments were presented to illustrate the theoretical result.