Abstract
This paper is concerned with the convergence problem of a recursive identifier for single-input single-output linear discrete-time stochastic systems with unknown constant parameters. The identifier was designed by introducing a compensator which satisfies a strictly positive real condition, and it includes the well-known recursive extended least squares method (the RELS method) as a special case of no compensator. Firstly, it is proved that the parameter estimates converge to its true values with probability one. Secondly, it is shown that the convergence analysis method given by Solo for the RELS method is not always applicable to the identifier because of the existence of the compensator, and that the evaluations given here on the rate of convergence and the identifiability condition become more precise than that given by the above analysis method.
