Two sided boundary stabilization of heterodirectional linear coupled hyperbolic PDEs

Jean Auriol (1) , Florent Di Meglio (1)

1 CAS - Centre Automatique et Systèmes

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems using actuation at both boundaries of the spatial domain. We design a novel Fredholm transformation similarly to backstepping approaches to derive a boundary controller and a boundary observer enabling stabilization by output feedback. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence to zero.

Domaines: Equations aux dérivées partielles [math.AP]; Automatique / Robotique

Jean Auriol, Florent Di Meglio. Two sided boundary stabilization of heterodirectional linear coupled hyperbolic PDEs. IEEE Transactions on Automatic Control, inPress, ⟨10.1109/TAC.2017.2763320⟩. ⟨hal-01318708v3⟩