Stabilizability of Time-Periodic Evolution Equations by Finite Dimensional Controls.

We study the stabilizability of time-periodic parabolic control systems with unbounded control operators. We give necessary and sufficient conditions for stabilizability which extend to the case of unbounded control operators, and which sharpen, conditions existing in the literature in the case of bounded control operators. We further show how to construct families of finite dimensional controls which preserves the stabilizability of the original system.