Feedback stabilization of linear and bilinear unbounded systems in Banach space

We consider linear control systems of the form ẋ(t)=Ax(t)−μBCx(t) where μ is a positive real parameter, A state operator and generates C0−semigroup contractions S(t) on Banach space X, B C are respectively operators observability, which defined in appropriate spaces they unbounded some sense. aim to show exponential stability above system under sufficient conditions expressed terms admissibility observability properties. The uniform stabilization using bilinear considered as well. Applications transport heat equations also provided.