Equivalent Conditions for Stabilizability of Infinite-Dimensional Systems withAdmissible Control Operators

摘要

In this paper, we study the stabilizability of infinite-dimensional systems withadmissible control operators. We show that under a weak condition such a system is stabilizable if and only if the system can be split into an exponentially stable system and a system which is exactly controllable in finite time. The unstable system is possibly infinite-dimensional. Furthermore, the unstable poles of a stabilizable system have to satisfy a certain summability condition.