Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input

A compensator design is proposed for a large class of parabolic distributed systems. Basically, it is a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design. The observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation. Explicit sufficient conditions are given for the convergence of this scheme.