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T. Nambu, “Stabilization and a Class of Functionals for Linear Parabolic Control Systems,” Proceedings of Royal Society Edinburgh, Section A, Vol. 140, No. 1, 2010, pp. 153-174. http://dx.doi.org/10.1017/S0308210508000978

has been cited by the following article:

• 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.