TITLE:
On Decay of Solutions and Spectral Property for a Class of Linear Parabolic Feedback Control Systems
AUTHORS:
Takao Nambu
KEYWORDS:
Stabilization of Linear Parabolic Systems; Decay of Functionals; Dynamic Feedback Scheme; Spectral Structures of Composite Systems; Complete Observability of Systems
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.9A,
December
18,
2013
ABSTRACT: 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.