Galerkin approximations of infinite-dimensional compensators for flexible structures with unbounded control action

Galerkin (finite elements) approximations of compensators/estimators for partially observed infinite-dimensional systems with unbounded control operators are considered. It is shown that these approximations enjoy two features: (i) they provide a near-optimal performance, and (ii) they retain uniform asymptotic stability properties (uniform with respect to the parameter of discretization) of the entire closed loop system. Examples of hyperbolic equations with boundary controls and boundary observations are provided.