This paper considers the task of constructing a linear model of the object studied using a robust criterion. The functionality applied, in this case, is correntropy. That makes it possible to obtain estimates that have robust properties. The evaluation algorithm is a multi-step procedure that employs a limited number of information measurements, that is, it has limited memory. The feature of the algorithm is that the matrices and observation vectors involved in estimate construction are formed in the following way: they include information about the newly arrived measurements and exclude information about the oldest ones. Depending on the way these matrices and vectors are built (new information is added first, and then outdated is excluded, or the outdated is first excluded, and then a new one is added), two estimate forms are possible. The second Lyapunov method is used to study the convergence of the algorithm. The conditions of convergence for a multi-step algorithm have been defined. The analysis of the established regime has revealed that the algorithm ensures that unbiased estimates are obtained. It should be noted that all the estimates reported in this work depend on the choice of the width of the nucleus, the information weighting factor, and the algorithm memory, the task of determining which remains open. Therefore, these parameters' estimates should be applied for the practical use of such multi-step algorithms. The estimates obtained in this paper allow the researcher to pre-evaluate the possibilities of identification using a multi-step algorithm, as well as the effectiveness of its application when solving practical tasks.

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