Boundary stabilization of a 1-D wave equation with multi-point velocity recirculations

Abstract

This paper considers the boundary state and output feedback stabilization of a one-dimensional wave equation with in-domain velocity feedbacks/recirculations of multi-intermediate points respectively. Constructing an auxiliary control system with nonlocal terms which are the displacements at the same intermediate points, we design a state feedback controller for the original system by a two-step backstepping transformation. The resulting closed-loop of original system is proved to be well-posed and exponentially stable. Then an observer-based output feedback controller is proposed to exponentially stabilize the original system. Finally, some numerical simulations are presented to validate the theoretical results.