Riesz basis and exact controllability of C0-groups with one-dimensional input operators

This paper considers the controllability and Riesz basis generation property of linear infinite dimensional systems with C0-group generators and one-dimensional admissible input operators. The corresponding results of [Advances in Mathematical Systems Theory, 2000, pp. 221-242] under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the eigenvalues are allowed to be algebraically multiple but with uniform boundedness of multiplicity.