Observability of linear discrete-time systems with different fractional orders

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send Rafał Kociszewski Faculty of Electrical Engineering, Białystok University of Technology, Poland

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Abstract

In the paper the observability problem for the linear discrete-time positive systems with different fractional orders is presented. Necessary and sufficient conditions for observability of this class of dynamical systems are given. A method for computing the initial state is proposed. Considerations are illustrated by theoretical example. Numerical calculations have been performed in the MATLAB program environment.

Keywords

discrete-time, fractional order, observability, positive, system

Obserwowalność liniowych układów dyskretnych różnych niecałkowitych rzędów

Streszczenie

W pracy rozpatrzono problem obserwowalności układów dyskretnych dodatnich przy różnych niecałkowitych rzędach w równaniu stanu. Podano warunki konieczne i wystarczające obserwowalności rozpatrywanej klasy układów dynamicznych. Zaproponowano prostą metodę wyznaczania nieujemnego stanu początkowego takiego układu. Rozważania zilustrowano przykładem teoretycznym, zaś niezbędne obliczenia wykonano w środowisku programowym MATLAB.

Słowa kluczowe

dodatni, obserwowalność, rząd niecałkowity, układ dyskretny

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