Intrinsic stability-control method for recursive filters and neural networks

Linear recursive filters can be adapted on-line but with instability proble ms, Stability-control techniques exist, hut they are either computationally expensive or nonrobust. For the nonlinear case, e.g., locally recurrent ne ural networks, the stability of infinite-impulse response (IIR) synapses is often a condition to be satisfied. This brief considers the known reparametrization-for-stability method for t he on-lint adaptation of IIR adaptive filters. A new technique is also pres ented, based on the further adaptation of the squashing function, which all ows to improve the convergence performance. The proposed method ran be appl ied to various filter realizations (direct Forms, cascade or parallel of se cond order sections, lattice form), as well as to locally recurrent neural networks, such as the IIR multi-layer perceptron (IIR-MLP), with improved p erformance with respect to other techniques and to the case of no stability control. In this brief the case of normalized lattice filters is particula rly considered; an analysis of the stabilization effects is also presented both analytically and experimentally.