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4 Bulletin of the Polish Academy of Sciences. Technical Sciences

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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.

The pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems

Kaczorek T., Sajewski Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2020

Vol. 68, nr 6

1513--1516

Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems are established. It is shown that if the fractional system is pointwise complete in one step (q = 1), then it is also pointwise complete for q = 2, 3…

Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

Sajewski Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 5

709--714

Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.

Descriptor fractional discrete-time linear system with two different fractional orders and its solution

Sajewski Ł.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2016

Vol. 64, nr 1

15--20

Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.