Positive minimal realizations of continuous-discrete linear systems with transfer function with separable denominator or numerator

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send Łukasz Sajewski Faculty of Electrical Engineering, Białystok University of Technology, Poland

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Abstract

The positive minimal realization problem for continuous-discrete linear single-input, single-output (SISO) systems is formulated. Two special case of the continuous-discrete systems are analyzed. Method based on the state variable diagram for nnding positive minimal realizations of given proper transfer functions is proposed. Sufficient conditions for the existence of positive minimal realizations of given proper transfer functions with separable numerator or transfer functions with separable denominator are established. Two procedures for computation of positive minimal realizations are proposed and illustrated by numerical examples.

Keywords

computation, continuous-discrete, existence, minimal, positive, realization

Wyznaczanie dodatnich realizacji minimalnych układów ciągło-dyskretnych o transmitancji z separowanym licznikiem lub mianownikiem

Streszczenie

Sformułowany został problem wyznaczania dodatniej realizacji minimalnej dla klasy liniowych układów ciągło-dyskretnych. Przeanalizowane zostały dwa przypadki szczególne układów ciągło-dyskretnych. Zaproponowana została metoda, bazująca na schemacie zmiennych stanu, wyznaczania dodatniej realizacji minimalnej na podstawie znanej transmitancji operatorowej układu. Określono warunki wystarczające istnienia dodatniej realizacji minimalnej dla transmitancji operatorowej z separowanym licznikiem lub mianownikiem. Podano dwie procedury wyznaczania dodatniej realizacji minimalnej, których efektywność zobrazowano przykładami numerycznymi.

Słowa kluczowe

dodatni, minimalna, realizacja, układ ciągło-dyskretny, wyznaczanie

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