Adaptive IIR Filtering and Output Error Identification: Robustness Analysis

Abstract

Recently, global convergence and parameter consistency of a certain parallel model adaptation algorithm in the presence of additive colored noise was established in [1]. In this paper, we examine the robustness of this algorithm, whose design is based on stochastic considerations, to bounded disturbances and unmodeled dynamics. We show that this algorithm is robust with respect to bounded disturbances and unmodeled dynamics whenever the denominator polynomial of the nominal model satisfies a strictly positive real (SPR) condition. We also show that the admissible class of unmodeled dynamics allows the true system to violate such an SPR condition. Similar robustness results are also proved for a non-vanishing gain update law.