ОБ УСТОЙЧИВОМ ПРЕЦИЗИОННОМ МОДЕЛИРОВАНИИ ОПЕРАТОРА ЗАПАЗДЫВАНИЯ.

The article is devoted to the research of delay operator modeling features using Taylor and Pade series. The purpose of the research is to determine the stability boundaries for approximation of the delay operator by Taylor series when the number of terms in the series is increasing. The scientific significance of the research states the Taylor series applicability conditions for the delay operator modelling. The conditions are important for modern software that allows precise modeling of complex systems. The Routh criterion is used to determine the stability boundaries. The calculations of the delay operator approximation poles for different number of series terms and the delay value were made. The scientific value of the research is the conclusion that the proof of corresponding functional series convergence is insufficient to use this series in modelling systems. The convergence of series does not guarantee the approximation stability and, respectively, applicability of the series. The practical value of the work results is grounded on the requirement to investigate not only convergence of the series, but also the approximation stability taking into account the approximation order and the operator parameters. [ABSTRACT FROM AUTHOR]