Feedback stabilization for unbounded bilinear systems using bounded control

摘要

In this paper, we deal with the distributed bilinear system dz(t)/dt = Az(t) + v(t)Bz(t), where A is the infinitesimal generator of a semigroup of contractions on a real Hilbert space H. The linear operator B is supposed bounded with respect to the graph norm of A. Then we give sufficient conditions for weak and strong stabilizations. Illustrating examples are provided.