Two important convergence properties of Lyapunov-theorybased adaptive filtering (LAF) adaptive filters are first explored. The LAF finite impulse response and infinite impulse response adaptive filters are then realized using the radial basis function (RBF) neural networks (NNs). The proposed adaptive RBF neural filtering system possesses the distinctive properties of RBF NN and the LAF filtering system. Unlike many adaptive filtering schemes using gradient search techniques, a Lyapunov

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... of the error between the desired signal and the RBF NN output is first defined. By properly choosing the weights update law in the Lyapunov sense, the RBF filter output can asymptotically converge to the desired signal. The design is independent of the stochastic properties of the input disturbances and the stability is guaranteed by the Lyapunov stability theory. Simulation examples for nonlinear adaptive prediction of nonstationary signal and system identification are performed. Index Terms-Adaptive filtering, Lyapunov stability theory, radial basis function neural network.