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1

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

Sajewski Ł.

Pomiary Automatyka Robotyka

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2013

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R. 17, nr 2

333-339

EN

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.

PL

Sformułowany został problem wyznaczania dodatniej realizacji minimalnej dla klasy liniowych układów ciągło-dyskretnych. Przeanalizowane zostały dwa przypadki szczególne układów ciągłodyskretnych. 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.

2

Positive Minimal Realization of Continuous-Discrete Linear Systems with All-Pole and All-Zero Transfer Function

Sajewski Ł.

Acta Mechanica et Automatica

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2013

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Vol. 7, no. 1

42-47

EN

The positive and minimal realization problem for continuous-discrete linear single-input and single-outputs (SISO) systems is formulated. Two special case of the continuous-discrete systems are given. Method based on the state variable diagram for finding a positive and minimal realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive minimal realization of a given proper transfer function of all-pole and all-zero systems are established. Two procedures for computation of a positive minimal realization are proposed and illustrated by a numerical examples.

3

Large minimal irregular digraphs

Dziechcińska-Halamoda Z., Majcher Z., Michael J., Skupień Z.

Opuscula Mathematica

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2003

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Vol. 23

21-24

EN

A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal if the removal of any arc results in a non-irregular digraph. A large minimal irregular digraph Fn of order n is constructed if n is the sum of initial positive integers. It is easily seen that the minimum and maximum sizes among n-vertex irregular digraphs are asymptotic to [formula] and n2, respectively. It appears that the size of Fn is asymptotic to n2, too. Similarly, a minimal irregular oriented graph Hn is constructed such that the size of Hn is asymptotic to 1/2n2 whence it is asymptotically the largest size among n-vertex oriented graphs whether irregular or not.