Distributed geometric control of infinite dimensional systems described by the Korteweg-de Vries-Burgers equation

In this study, the late lumping geometric control of a Korteweg-de Vries-Burgers equation with periodic boundary conditions is investigated. A distributed state feedback is designed following the input-output linearization approach based on the characteristic index. The controlled variable represents the weighted spatial average of the state while the actuation is distributed along the space domain. It is shown, based on the variational lemma, that the state feedback provides a stable closed loop system in
$L_{2}$
-norm. The stabilization performance, a particular case of the output tracking problem, is evaluated via simulation runs in the case of the wave suppression problem. The simulation performed demonstrated the performance of the developed state feedback in tracking the reference.