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1
Content available 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
EN
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.
2
Content available New stability tests for positive descriptor linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 3
art. no. e140688
EN
The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.
3
Content available 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
EN
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.
4
Content available 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
EN
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…
5
Content available Computation of positive realizations for descriptor linear continuoustime systems
Kaczorek T.
Autobusy : technika, eksploatacja, systemy transportowe
|
2018
|
R. 19, nr 12
428--432
EN
A new method for computation of positive realizations of given transfer matrices of descriptor linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
PL
W pracy podano nową metodę wyznaczania dodatnich realizacji dla zadanych macierzy transmitacji operatorowych deskryptowych( singularnych) ciągłych układów liniowych. Sformułowano warunki konieczne i wystarczające istnienia dodatnich realizacji dla tej klasy deskryptowych ciągłych układów liniowych. Podano procedurę wyznaczania tych realizacji. Procedura ta została zlustrowana przykładami liczbowymi.
6
Content available Superstabilization of positive linear electrical circuit by state-feedbacks
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2017
|
Vol. 65, nr 5
703--708
EN
The concept of superstability of positive linear electrical circuits is introduced and its properties are characterized. The superstabilization of positive and nonpositive electrical circuits by state-feedbacks is analyzed.
7
Content available 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
EN
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.
8
Content available Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2017
|
Vol. 65, nr 3
305--311
EN
The stability of fractional standard and positive continuous-time linear systems with state matrices in integer and rational powers is addressed. It is shown that the fractional systems are asymptotically stable if and only if the eigenvalues of the state matrices satisfy some conditions imposed on the phases of the eigenvalues. The fractional standard systems are unstable if the state matrices have at least one positive eigenvalue.
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