Stabilization of a linear 2 × 2 hyperbolic system with uncertain parameters from anti-collocated sensing and control

Using a series of invertible transformations, we bring a system of 2 × 2 linear hyperbolic partial differential equations (PDEs) to an observer canonical form. With transport delays as the only information assumed known about the system parameters, a filter based adaptive output feedback control law is designed for the transformed system. Pointwise boundedness of all signals in the closed loop system and pointwise convergence of the system states to zero are established. The theory is demonstrated in a simulation.