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Summary The scope of this research is a problem of parameters identification of a linear time‐invariant plant, which (1) input signal is not frequency‐rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above‐stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least‐squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above‐mentioned properties are mathematically proved and demonstrated via simulation experiments.