Feedback Stabilization Over a First Order Moving Average Gaussian Noise Channel
Middleton, Richard H. and Rojas, Alejandro J. and Freudenberg, James S. and Braslavsky, Julio H. (2009) Feedback Stabilization Over a First Order Moving Average Gaussian Noise Channel. IEEE Transactions on Automatic Control, 54 (1). pp. 163-167. ISSN 0018-9286
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 z = ø(with |ø| >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 Cfb ≥ log2 |ø|. 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 Cfb ≥ log2 |ø|.
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