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Necessary and Sufficient Conditions for Stability of LMS
Chinese Academy of Sciences, China.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
The Central University for Nationalities, China.
1997 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 42, no 6, 761-770 p.Article in journal (Refereed) Published
Abstract [en]

Guo and Ljung (1995) established some general results on exponential stability of random linear equations, which can be applied directly to the performance analysis of a wide class of adaptive algorithms, including the basic LMS ones, without requiring stationarity, independency, and boundedness assumptions of the system signals. The current paper attempts to give a complete characterization of the exponential stability of the LMS algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded, nonstationary, and non-φ-mixing signals. The results of this paper can be applied to a very large class of signals, including those generated from, e.g., a Gaussian process via a time-varying linear filter. As an application, several novel and extended results on convergence and the tracking performance of LMS are derived under various assumptions. Neither stationarity nor Markov-chain assumptions are necessarily required in the paper.

Place, publisher, year, edition, pages
1997. Vol. 42, no 6, 761-770 p.
Keyword [en]
Least mean squares methods, Numerical stability, Signal processing, Tracking
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-56366DOI: 10.1109/9.587328OAI: diva2:318582
Swedish Research Council
Available from: 2010-05-08 Created: 2010-05-07 Last updated: 2013-07-16

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