Wyznaczanie realizacji dodatniej liniowego układu hybrydowego typu SISO w postaci drugiego modelu Fornasiniego-Marchesiniego

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send Łukasz Sajewski Politechnika Białostocka Wydział Elektryczny

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Streszczenie

Sformułowano problem realizacji dla hybrydowych dodatnich układów liniowych o jednym wejściu i jednym wyjściu (SISO), w postaci drugiego modelu Fornasiniego-Marchesiniego. Zaproponowano metodę wyznaczania realizacji dodatniej dla danej transmitancji właściwej w oparciu o schemat zmiennych stanu. Podano warunki wystarczające na istnienie realizacji dodatniej dla danej transmitancji właściwej. Sformułowano również procedurę wyznaczania realizacji dodatniej, którą zilustrowano przykładem numerycznym.

Słowa kluczowe

model Fornasiniego-Marchesiniego, układ hybrydowy, układ liniowy

Computation of positive realization of hybrid linear SISO systems described by the second Fornasini-Marchesini model

Abstract

The realization problem for positive linear hybrid systems with single input and single output (SISO), described by the second Fornasini-Marchesini model is formulated. The method based on the state variable diagram for finding a positive realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive realization of a given proper transfer function are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.

Keywords

Fornasini-Marchesini model, hybrid system, linear system

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