Output regulation of anti-stable coupled wave equations via the backstepping technique

This study is concerned with the output regulation of an anti-stable system of coupled wave equations with external disturbances. A state-feedback regulator is designed to force the output of the coupled wave equations to track the reference signal, which is generated by an exosystem. Moreover, the tracking error decays exponentially at a prescribed rate. The design is based on backstepping approach and relies on solving the regulator equations. The solvability condition of the regulator equations is characterised by the transfer matrix of the coupled wave equations and eigenvalues of the exosystem. An output-feedback regulator is then constructed by developing an observer. Finally, the numerical simulations are demonstrated for the effectiveness of the theoretical results.