In 1998, A. Karimi and I.D. Landau published in the journal "Systems and Control letters" an article entitled "Comparison of the closed-loop identification methods in terms of bias distribution". One of its main purposes was to provide a bias distribution analysis in the frequency domain of closed-loop output error identification algorithms that had been recently developed. The expressions provided in that paper are only valid for prediction error identification methods (PEM), not for pseudo-linear regression (PLR) ones, for which we give the correct frequency domain bias analysis, both in open-and closed-loop. Although PLR was initially (and is still) considered as an approximation of PEM, we show that it gives better results at high frequencies.

In this paper, we extend convergence conditions for the parameter adaptation algorithm, used in discrete-time recursive identification schemes, or in adaptive control. Whereas the classical stability analysis of this algorithm consists in checking the strictly real positiveness of an associated transfer function, we demonstrate that convergence can be obtained even when this condition is not fulfilled, under some assumptions on the algorithm forgetting factors. These results regarding both deterministic and stochastic contexts are obtained by analyzing convergence with a prescribed degree of stability.

The stability of an adaptive disturbance rejection scheme based on the Youla-Kucera parameterization is investigated, in case of an uncertain plant model is used in the synthesis of the central controller. It is shown that stability is guaranteed provided that two conditions are satisfied at the same time: the first one is linked to the internal model principle, and the second one depends on the closed-loop poles location. For some uncertainties, these constraints cannot be met simultaneously with the minimal Q-filter. That leads to propose an over-parametrized Youla-Kucera filter, in order to relax the said conditions. Simulations on relevant examples illustrate the procedure for stabilizing the Youla-Kucera adaptive rejection scheme, in the presence of plant model uncertainties.This work was not supported by any organization B.Vau is with SATIE,école normale supérieure de Paris-Saclay, 94230 Cachan, France and with IXBLUE, 12 avenue des coquelicots 94385 Bonneuil-sur-Marne,