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On Decay of Solutions and Spectral Property for a Class of Linear Parabolic Feedback Control Systems
Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, Kobe, Japan
- 1 Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, Kobe, Japan
Advances in Pure Mathematics·Volume 03 (2013)·Pages 26–37·Published 29 November 2013·DOI10.4236/apm.2013.39A1005
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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 function al s 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.
KeywordsStabilization of Linear Parabolic SystemsDecay of FunctionalsDynamic Feedback SchemeSpectral Structures of Composite SystemsComplete Observability of Systems
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