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The scope of this research is a problem of parameters identification of alinear time-invariant (LTI) plant, which 1) input signal is not frequency-rich,2) is subjected to initial conditions and external disturbances. The memoryregressor extension (MRE) scheme, in which a specially derived differentialequation 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 acondition of the initial excitation (IE) is met. Using the MRE scheme, therecursive least-squares (RLS) method with the forgetting factor is used toderive an adaptation law. The following properties have been proved for theproposed approach. If the IE condition is met, then: 1) the parameter error ofidentification is a limited value and converges to zero exponentially (if thereare no external disturbances) or to a bounded set (in the case of them) with anadjustable rate, 2) the parameters adaptation rate is a finite value. Theabove-mentioned properties are mathematically proved and demonstrated viasimulation experiments.

Robust method to provide exponential convergence of model parameters solving LTI plant identification problem