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In the theory of mathematical modeling of nonlinear dynamic systems the universal technique of Volterra functional series is well known (Volterra, 1982). It presents a response 
of the input-output system to an external disturbance 
(for simplicity consider 
and 
to be scalar time functions) as the integro-power series:
(1)In (1) the functions 
, that are called Volterra kernels, are identified on the basis of information about system responses to certain families of test input signals.
Application of the finite segment of series (1):
(2) to modeling of nonlinear dynamic objects of various nature is based on continual analogs of the classical Weierstrass theorem about approximation of continuous function by polynomial, i.e. Frechet theorem (Frechet, 1910) and its different generalizations. For example, according to Baesler and Daugavert (1990) for any Volterra initial (
) mapping
– compact in
and any
there is
such that for all
the equality:
holds, where
has the form (2).
The problem of applying the Volterra series to modeling of technical systems (in particular electric power and heat supply systems) was considered in the monographs (Pupkov, Kapalin & Yushchenko, 1976; Deitch, 1979; Venikov & Sukhanov, 1982; Pupkov & Shmykova, 1982; Danilov, Matkhakov & Filippov, 1990). The international sources to be emphasized are the profound monographs (Rugh, 1981; Doyle III, Pearson & Ogunnaike, 2002; Ogunfunmi, 2007) that provide an extensive bibliography.