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3 Bulletin of the Polish Academy of Sciences. Technical Sciences

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Positivity and cyclicity of descriptor electrical circuits with chain structure

Kaczorek Tadeusz, Borawski Kamil

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 1

art. no. e139955

The positivity and cyclicity of descriptor linear electrical circuits with chain structure is considered. Two classes of descriptor linear electrical circuits are analyzed. Some new properties of these classes of electrical circuits are established. The results are extended to fractional descriptor linear electrical circuits.

A new extension of the Cayley-Hamilton theorem to fractional different orders linear systems

Kaczorek Tadeusz

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 2

art. no. e139960

The classical Cayley–Hamilton theorem is extended to fractional different order linear systems. The new theorems are applied to different orders fractional linear electrical circuits. The applications of new theorems are illustrated by numerical examples.

Positive electrical circuits with the chain structure and cyclic Metzler state matrices

Kaczorek Tadeusz

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 4

art. no. e137731

The cyclicity of the state matrices of positive linear electrical circuits with the chain structure is considered. Two classes of positive linear electrical circuits with the chain structure and cyclic Metzler state matrices are analyzed. Some new properties of these classes of positive electrical circuits are established. The results are extended to fractional linear electrical circuits.