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Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay exactly faster than . The system contains a dynamic compensator with another state v in the feedback loop, and consists of two states u and v. This problem entirely differs from the one with static feedback scheme in which the system consists only of a single state u. To show the essential difference, some specific property of the spectral subspaces associated with our control system is studied.

On Decay of Solutions and Spectral Property for a Class of Linear Parabolic Feedback Control Systems