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1
Content available Transfer matrices with positive coefficients of descriptor linear systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
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2024
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Vol. 6, No. 1
7--17
EN
Transfer matrices with positive coefficients of descriptor positive linear continuous-time systems are addressed. Two methods of checking of the positivity of descriptor linear systems are proposed. It is shown that if the positive descriptor system is asymptotically stable then all coefficients of its transfer matrix are positive.
2
Content available Shuffle algorithm for fractional descriptor Roesser type continuous-time linear systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
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2022
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Vol. 4, No. 1
7--12
EN
The shuffle algorithm is applied to analysis of the fractional descriptor Roesser type continuous-time linear systems. Using the shuffle algorithm the fractional descriptor linear system is reduced to the equivalent standard system and the system is decomposed into dynamic and static parts. Procedure for computation of the matrices of equivalent standard system and of the dynamical and static parts of the system is proposed.
PL
Algorytm przesuwania jest stosowany do analizy ułamkowych deskryptorowych układów liniowych ciągłych typu Roesser. Stosując algorytm przesuwania, liniowy układ deskryptorowy niecałkowitego rzędu jest redukowany do równoważnego układu standardowego, oraz jest rozkładany na część dynamiczną i statyczną. Zaproponowano procedurę obliczania macierzy równoważnego układu standardowego oraz metodę obliczania części dynamicznej i statycznej.
3
Content available Global stability of positive discrete-time time-varying nonlinear feedback systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
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2021
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Vol. 3, No. 1
17--20
EN
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
4
Content available Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders
Kaczorek Tadeusz, Sajewski Łukasz
International Journal of Applied Mathematics and Computer Science
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2020
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Vol. 30, no. 4
641--647
EN
Descriptor and standard linear continuous-time systems with different fractional orders are investigated. Descriptor systems are analyzed making use of the Drazin matrix inverse. Necessary and sufficient conditions for the pointwise completeness and pointwise degeneracy of descriptor continuous-time linear systems with different fractional orders are derived. It is shown that (i) the descriptor linear continuous-time system with different fractional orders is pointwise complete if and only if the initial and final states belong to the same subspace, (ii) the descriptor linear continuous-time system with different fractional orders is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Results are reported for the case of two different fractional orders and can be extended to any number of orders.
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