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

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DOI: 10.4236/apm.2013.39A1005    2,560 Downloads   3,975 Views  
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

T. Nambu, "On Decay of Solutions and Spectral Property for a Class of Linear Parabolic Feedback Control Systems," Advances in Pure Mathematics, Vol. 3 No. 9A, 2013, pp. 26-37. doi: 10.4236/apm.2013.39A1005.

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