Strong Stabilizability of Infinite Dimensional Linear Systems

The questions of strong stabilizability of general linear systems in Hilbert space of the form x = Ax + Bu are considered. The operator A may not generate a C0-semigroup of contraction(or even C0-semigroup) in Hilbert space X but it could be decomposed into two parts. That is, A = A0 + Ap where A0 is the generator of C0-semigroup of contraction and Ap is the rest part of system operators(or considered as perturbation of A0) which may be bounded or unbounded, and B is a bounded linear operator from another Hilbert space U to X. Sufficient conditions are presented that guarantee stabilizability of the linear system based on the results developed in [8]. The theories are illustrated by two examples involving heat equation and wave equation with numerical results.