Boundary Exponential Stabilization of 1-Dimensional Inhomogeneous Quasi-Linear Hyperbolic Systems

Abstract

This paper deals with the problem of boundary stabilization of first-order $n\times n$ inhomogeneous quasi-linear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design multiboundary feedback controllers to achieve exponential stability with arbitrary decay rate of the original nonlinear system in the spatial $H^2$ sense.