Stabilization of linear 2 × 2 hyperbolic systems with uncertain coupling coefficients - part I: Identifier-based design

We design a state feedback control law to adaptively stabilize a 2 × 2 linear hyperbolic system of partial differential equations (PDEs) with uncertain in-domain coupling coefficients. We do this by combining an identifier with a backstepping-based controller and show boundedness and integrability in the ℒ ₂ -sense of all signals in the closed loop system. The theory is demonstrated in a simulation.