Conditions for stabilizability of distributed parameter systems

The authors consider distributed parameter control systems of the form dx(t)/dt=Ax(t)+Bu(t ). They address the question of finding necessary conditions for there to exist an operator K such that A+BK is exponentially stable. S.A. Nefedov and F.A. Sholokhovich (1986) have answered this question when B is bounded and the control space is finite-dimensional. The present authors extend this result to the case where the control space is not necessarily finite dimensional and BK is A-bounded. They then apply this result to boundary stabilization of a rectangular vibrating plate