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

This paper considers linear infinite dimensional systems with C-0-group generators and one-dimensional admissible input operators. The exact controllability and Riesz basis generation property are discussed. The corresponding results of Jacob and Zwart (Advances in Mathematical Systems Theory, Birkhauser, Boston, MA, 2000) 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 a uniform bound on the multiplicity. (C) 2003 Elsevier B.V. All rights reserved.