  The scope of this research is a problem of parameters identification of a
linear time-invariant (LTI) 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 limited regressor value, for which a
condition of the initial excitation (IE) is met. Using the MRE scheme, the
recursive least-squares (RLS) 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 a limited value and converges to zero exponentially (if there
are no external disturbances) or to a bounded 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.
