PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 71

Liczba wyników na stronie
first rewind previous Strona / 4 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  fractional
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 4 next fast forward last
1
Content available Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2023
|
Vol. 5, No. 1
8--19
EN
The Drazin inverse of matrices is applied to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor standard and fractional linear continuous-time and discrete-time systems. It is shown that: 1) The descriptor linear continuous-time system is pointwise complete if and only if the initial and final states belong to the same subspace. 2) The descriptor linear discrete-time system is not pointwise complete if its system matrix is singular. 3) System obtained by discretization of continuous-time system is always not pointwise complete. 4) The descriptor linear continuous-time system is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. 5) The descriptor fractional system is pointwise complete if the matrix defined by (36) is invertible. 6) The descriptor fractional system is pointwise degenerated if and only if the condition (41) is satisfied. Considerations are illustrated by examples of descriptor linear electrical circuits.
2
Content available New stability tests for fractional positive descriptor linear systems
Kaczorek Tadeusz, Ruszewski Andrzej
Archives of Control Sciences
|
2023
|
Vol. 33, No. 1
71--81
EN
The asymptotic stability of fractional positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.
3
Content available A comparative study of the sensitivity analysis for systems with viscoelastic elements
Łasecka-Plura Magdalena
Archive of Mechanical Engineering
|
2023
|
LXX, nr 1
5--25
EN
This paper discusses the different methods used for calculating first- and second-order sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.
4
Content available Standard and fractional discrete-time linear systems with zero transfer matrices
Kaczorek Tadeusz, Ruszewski Andrzej
Acta Mechanica et Automatica
|
2023
|
Vol. 17, no. 2
188--191
EN
The transfer matrix of the standard and fractional linear discrete-time linear systems is investigated. Necessary and sufficient conditions for zeroing of the transfer matrix of the linear discrete-time systems are established. The considerations are illustrated by examples of the standard and fractional linear discrete-time systems.
5
Content available Shuffle algorithm for fractional descriptor Roesser type continuous-time linear systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
|
2022
|
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.
6
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.
7
Content available 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
EN
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.
8
Content available Observers of fractional linear continuous-time systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2022
|
Vol. 32, No. 1
73--84
EN
The concepts of full-order and reduced-order observers are extended to the fractional linear continuous-time systems. Necessary and sufficient conditions for the existence of the observers for fractional linear systems are established. Procedures for designing of the observers are given and illustrated by examples.
9
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.
10
Content available Application of the Lagrange-Sylvester formula to computation of the solution to state equations of fractional linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2021
|
Vol. 69, nr 2
art. no. e136729
EN
The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems. The solutions are given as finite sums with their numbers of components equal to the degrees of the minimal characteristics polynomials of state matrices of the systems. Procedures for computations of the solutions are given and illustrated by numerical examples of continuous-time and discrete-time fractional linear systems.
11
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…
12
Content available Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks
Kaczorek T., Ruszewski A.
Archives of Control Sciences
|
2020
|
Vol. 30, No. 4
667--681
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.
13
Content available The pointwise completeness and the pointwise degeneracy of fractional descriptor discrete-time linear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 6
989--993
EN
The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear discrete-time systems are established. It is shown that every fractional descriptor linear discrete-time systems is not pointwise complete and it is pointwise degenerated in one step (for i= 1).
14
Content available Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems
Ruszewski A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 3
509--515
EN
The practical and asymptotic stabilities of delayed fractional discrete-time linear systems described by the model without a time shift in the difference are addressed. The D-decomposition approach is used for stability analysis. New necessary and sufficient stability conditions are established. The conditions in terms of the location of eigenvalues of the system matrix in the complex plane are given.
15
Content available Positivity of fractional descriptor linear continuous-time systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 2
229--233
EN
The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.
16
Content available Stability of discrete-time fractional linear systems with delays
Ruszewski Andrzej
Archives of Control Sciences
|
2019
|
Vol. 29, No. 3
549--567
EN
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
17
Content available (F, ρ)-invexity of higher order for multiobjective fractional variational problem
Kumar P., Sharma B.
Control and Cybernetics
|
2018
|
Vol. 47, no. 2
131--146
EN
Multiobjective fractional variational problem is considered and sufficient optimality conditions, characterizing efficiency of higher order, are obtained under the assumptions of (F,ρ)−invexity of higher order on the functionals involved. Parametric higher order dual of the above stated problem is proposed. Duality theorems are proved to relate efficient solutions of higher order for primal and its dual problem using generalized class of functionals.
18
Content available Characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders
Kaczorek T.
Acta Mechanica et Automatica
|
2018
|
Vol. 12, no. 3
209--216
EN
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders is addressed. It is shown that the characteristic equations of standard and descriptor linear electrical circuits are independent of the method used in their analysis: the state space method, the mesh method and the node method. The considerations are illustrated by examples of standard and fractional linear electrical circuits.
19
Content available remote Responses of standard and fractional linear systems and electrical circuits with derivatives of their inputs
Kaczorek T.
Przegląd Elektrotechniczny
|
2017
|
R. 93, nr 6
132--136
EN
The responses of continuous-time and discrete-time linear systems with derivatives of their inputs are addressed. It is shown that the formulae for state vectors and outputs are also valid for their derivatives if the inputs and outputs and their derivatives of suitable order are zero for t = 0. Similar results are also shown for the discrete-time linear systems and for the fractional continuous-time and discrete-time linear systems.
PL
W artykule rozpatrywane są ciągłe układy i obwody elektryczne liniowe oraz dyskretne układy liniowe z pochodnymi (i odpowiednio różnicami) wymuszeń. Pokazano, że wzory określające pochodne wyjścia układów i wektorów stanu są również prawdziwe dla ich pochodnych jeżeli odpowiednie warunki początkowe i ich pochodnych są zerowe. Analogiczne wyniki zostały również wyprowadzone dla układów dyskretnych rzędów całkowitych i niecałkowitych.
20
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.
first rewind previous Strona / 4 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.