A stable family of adaptive IIR filters

This paper unifies a rapidly growing area of inquiry: adaptive infinite impulse response (IIR) filter development and evaluation. A class of stably convergent adaptive IIR filters has evolved from a proven adaptive IIR filter with an auto-regressive, moving-average (ARMA) structure. The convergence proof was originally based on a hyperstability evaluation of an identification format. This paper relates this format to those arising from other applicable nonlinear stability theory results. These interrelationships allow statement of a growing list of adaptive IIR filter properties. The alternate search/minimization technique of adaptive IIR filler development is also derived and contrasted. This results in a proposal of a general adaptive filter algorithm.