Intrinsic stability-control method for recursive filters and neural networks

Linear recursive filters can be adapted on-line but with instability problems. Stability-control techniques exist, but they are either computationally expensive or nonrobust. For the nonlinear ease, e.g., locally recurrent neural 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 the on-line adaptation of IIR adaptive filters. A new technique is also presented, based on the further adaptation of the squashing function, which allows one to improve the convergence performance. The proposed method can be applied to various filter realizations (direct forms, cascade or parallel second order sections, lattice form), as well as to locally recurrent neural networks, such as the IIR multi-layer perceptron (IIR-MLP), with improved performance with respect to other techniques and to the case of no stability control. In this brief, the case of normalized lattice filters is particularly considered; an analysis of the stabilization effects is also presented both analytically and experimentally.