Stabilization of a linear hyperbolic system with one boundary controlled transport PDE coupled with n counterconvecting PDEs

Abstract

We propose a full-state feedback law to stabilize linear first-order hyperbolic systems featuring n positive and one negative transport speeds on a finite space domain. Only one state, corresponding to the negative velocity, is actuated at the right boundary. The proposed controller guarantees convergence of the whole (n + 1)-state system to zero in the L2-sense.