Collocated output-feedback stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping

Abstract

We consider the problem of output feedback stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs with boundary actuation and measurement. We design an output feedback control law, with actuation and measurement on only one end of the domain, and prove local H2 exponential stability of the closed-loop system. The proof of stability is based on the construction of a strict Lyapunov function which includes the observer states. The feedback law and output injection gains are found using the backstepping method for 2 × 2 system of first-order hyperbolic linear PDEs, developed by the authors in a previous work, which is briefly reviewed.