Обращение линейных динамических систем в классе полиномиальных сигналов

Abstract

Предложен метод и алгоритм решения задачи обращения линейных динамических систем в среде полиномиальных сигналов. Решение задачи получено на основе матричных представлений полиномиальных вектор - функций входа, выхода и состояния и статических матричных преобразований, что позволило свести поставленную задачу к решению линейной системы алгебраических уравнений. Предложен метод анализа робастности полученных результатов. Разработано соответствующее программное обеспечение.There has been proposed a method, algorithm and software solving the problem of inversion of linear dynamical systems in the polynomial signal environment. The solution of the problem was obtained on the basis of matrix representations of polynomial input, output, and state vector functions and static matrix transformations, which made it possible to reduce the problem posed to the solution of a linear system of algebraic equations. Also, there has been proposed a method for analyzing the robustness of the results obtained. There has been developed the software for implementing the proposed methods. The software includes the approximation of the initial information by polynomials of a given degree by the method of least squares, the formation of matrix analogs of the polynomial task by the output of the system, the formation of a matrix of a system of linear algebraic equations, and its solution. The maximum degree of approximating polynomials is corrected on the basis of estimation of the number of conditionality. The software contains a block for estimating the accuracy of the result of the call.