Fundamental Issues in the Stability of Adaptive IIR Filters

Adaptive IIR filter analysis is more complicated than for the FIR case because (a) some algorithm signals are generated by the adaptive filter itself, and (b) the prediction error relates to the adapted parameters via a filtering operation. Averaging analyses of stability address the first issue by linearization about the convergence point, and the second by using passivity of the error operator. However, published results do not fully account for signal dynamics in the linearization, nor have initial conditions in the passivity analysis been considered. This paper addresses these gaps. Our motivation to revisit these broadly applicable issues is for analyzing recently developed adaptive algorithms that have application to biological systems.