A NOVEL CLASS OF BIBO STABLE RECURSIVE NONLINEAR FILTERS

In this paper, we introduce a novel class of nonlinear filters char-acterized by two interesting properties: (i) according to the Stone-Weierstrass approximation theorem, the proposed nonlinear filters are able to arbitrarily well approximate any discrete-time, time-invariant, causal, infinite-memory, continuous, nonlinear system; (ii) the filters are always stable according to the bounded-input-bounded-output criterion. This novel class includes as a subclass the finite-memory even mirror Fourier nonlinear filters, which have been recently introduced as an useful tool for modeling strong saturation nonlinearities. Index Terms — Nonlinear systems, linear-in-the-parameters nonlinear filters, universal approximators, BIBO stability