We study the wellposedness and the main features of a class of feedback control systems. The involved control system is composed of the generator of a strongly continuous group for the free part and of an unbounded control operator, so that the results can be applied to boundary or point control problems for partial differential equations of hyperbolic or Petrowski type. The feedback operator is explicit and one can achieve an arbitrary large decay rate for the closed-loop system. These results are proved under a controllability assumption and the proofs rely on general results about the algebraic Riccati equation associated with the linear quadratic regulator problem.