Feedback stabilization of distributed parameter systems by a functional observer

Feedback stabilization of unstable parabolic equations is of great interest. The fact that it is not necessarily possible to stabilize the equations by means of static feedback schemes when both observation and control can be realized only through the boundary is illustratively shown by a simple example. In view of this, a functional observer of Luenberger type is derived and then utilized in order to stabilize unstable parabolic equations for which observation of the state and control can be carried out only through the boundary.