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• W2155487796 abstract "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-/spl phi/-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." @default.
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• W2155487796 date "1997-06-01" @default.
• W2155487796 modified "2023-09-23" @default.
• W2155487796 title "Necessary and sufficient conditions for stability of LMS" @default.
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• W2155487796 doi "https://doi.org/10.1109/9.587328" @default.
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