State Feedback Regulator Design for Coupled Linear Wave Equations

Abstract

In this paper the state feedback regulator design is considered for a system of coupled linear wave equations with distinct constant wave speeds and a spatially-varying coupling. To this end, recent results for the backstepping control of coupled linear parabolic systems are extended to coupled linear wave equations. Subsequently, an additional feedforward controller is determined to ensure output regulation for reference inputs and disturbances described by a finite-dimensional signal model. The design of the resulting state feedback regulator is based on explicitly solving the regulator equations, for which a simple existence condition is provided. Exponential stability is verified for the closed-loop system. Two coupled wave equations subject to destabilizing boundary conditions are utilized to illustrate the results of the paper.