Output error identification without SPR assumptions

This paper uses an input-output stability analysis approach to show that for a large class of output error identification algorithms, the usual strict positive real (SPR) conditions on the unknown plant can be replaced by "persistent power" conditions on the plant input sequence. The only a priori knowlege of the plant assumed is stability and knowlege of a model order upper bound. This class of algorithms is shown to include the constant direction, recursive least squares with forgetting, controlled trace, and covariance resetting variants, extending the results of [1]. Arguments for the necessity of the SPR condition in other cases, eg. recursive least squares and stochastic approximation, are also given. Implications in identification and adaptive IIR filtering are discussed.