Output feedback stabilization of an underactuated cascade network of interconnected linear PDE systems using a backstepping approach

Abstract

We detail in this article the development of a robust stabilizing output feedback control law for an underactuated cascade network of n systems of two heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through their boundaries. Only one of the subsystems is actuated. The proposed approach combines successive backstepping transformations that present a specific cascade structure. With these transformations it is possible to rewrite the original network system as a simple system for which all the in-domain coupling terms have been removed. One can then design a strictly proper stabilizing control law. The proposed control law is proved to be robust to small delays in the actuation. Finally, a boundary observer is designed, enabling stabilization by output feedback.