Convergence and steady-state analysis of the normalized least mean fourth algorithm
Digital Signal Processing
Adaptive filters with error nonlinearities: mean-square analysis and optimum design
EURASIP Journal on Applied Signal Processing
Feedback analysis of U-model via small gain theorem
ACMOS'08 Proceedings of the 10th WSEAS International Conference on Automatic Control, Modelling & Simulation
MIMO U-model based control: real-time tracking control and feedback analysis via small gain theorem
WSEAS Transactions on Circuits and Systems
A class of stochastic gradient algorithms with exponentiated error cost functions
Digital Signal Processing
IEEE Transactions on Signal Processing
A strict stability limit for adaptive gradient type algorithms
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Steady-state analysis of the long LMS adaptive filter
Signal Processing
EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in theory and methods for nonstationary signal analysis
H∞-robustness of adaptive filters against measurement noise and parameter drift
Automatica (Journal of IFAC)
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This paper provides a time-domain feedback analysis of gradient-based adaptive schemes. A key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties (along the lines of H∞-theory and robust filtering). The analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions. It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes. The feedback structure is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The configuration is further shown to lend itself to analysis via a so-called small gain theorem, thus leading to stability and robustness conditions that require the contractivity of certain operators. Choices for the step-size parameter in order to guarantee faster rates of convergence are also derived, and simulation results are included to demonstrate the theoretical findings. In addition, the time-domain analysis provided in this paper is shown to extend the so-called transfer function approach to a general time-variant scenario without any approximations