Output-Feedback Stabilization for a Class of Linear Parabolic Systems

We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement of the state at each point in the domain. To this end, backstepping observers are designed for both anti-collocated and collocated sensors and actuators. Furthermore, we show the closed-loop systems consisting of the plant, the backstepping control laws, and the observer is exponentially stable. The backstepping method is used to obtain both control and observer kernels. The kernels are the solution of $4\times4$ systems of second-order hyperbolic linear PDEs whose well-posedness is shown.