Unbounded perturbation of the controllability for evolution equations ✩

In this paper we prove that the controllability for evolution equations in Banach spaces is not destroyed, if we perturb the equation by “small” unbounded linear operator. This is done by employing a perturbation principle from linear operator theory and a characterization of surjective operators in Banach spaces. Finally, we apply these to a control system governed by partial integrodifferential equations.  2003 Elsevier Science (USA). All rights reserved.