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• W2102893304 abstract "Recent developments in information theory by Y.-H. Kim have established the feedback capacity of a first order moving average additive Gaussian noise channel. Separate developments in control theory have examined linear time invariant feedback control stabilization under signal to noise ratio (SNR) constraints, including colored noise channels. This note considers the particular case of a minimum phase plant with relative degree one and a single unstable pole at <i xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>z</i> =phi (with |phi| > 1) over a first order moving average Gaussian channel. SNR constrained stabilization in this case is possible precisely when the feedback capacity of the channel satisfies <i xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>CFB</i> ges log <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> |phi|. Furthermore, using the results of Kim we show that there exist linear encoding and decoding schemes that achieve stabilization within the SNR constraint precisely when <i xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>CFB</i> ges log <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> |phi|." @default.
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• W2102893304 date "2009-01-01" @default.
• W2102893304 modified "2023-10-18" @default.
• W2102893304 title "Feedback Stabilization Over a First Order Moving Average Gaussian Noise Channel" @default.
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• W2102893304 doi "https://doi.org/10.1109/tac.2008.2007183" @default.
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