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Tytuł:
Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits
Autorzy:
Kaczorek, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/27309779.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Technologiczno-Humanistyczny im. Kazimierza Pułaskiego w Radomiu
Tematy:
descriptor
fractional
linear
electrical circuit
Drazin inverse
Opis:
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.
Źródło:
Journal of Automation, Electronics and Electrical Engineering; 2023, 5, 1; 21--34
2658-2058
2719-2954
Pojawia się w:
Journal of Automation, Electronics and Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Autorzy:
Beata, Sikora
Powiązania:
https://bibliotekanauki.pl/articles/27311455.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
descriptor systems
fractional-order systems
Caputo derivative
Drazin inverse
controllability
pochodna Caputo
odwrotność Drazina
sterowalność
system deskryptorowy
system ułamkowego rzędu
Opis:
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the Drazin inverse to the analysis of pointwise completeness and pointwise degeneracy of descriptor fractional linear continuous-time systems
Autorzy:
Kaczorek, Tadeusz
Ruszewski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/330993.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
pointwise completeness
pointwise degeneracy
fractional system
descriptor system
zupełność punktowa
degeneracja punktowa
system ułamkowy
system deskryptorowy
Opis:
The Drazin inverse of matrices is applied to the analysis of pointwise completeness and pointwise degeneracy of fractional descriptor linear continuous-time systems. It is shown that (i) descriptor linear continuous-time systems are pointwise complete if and only if the initial and final states belong to the same subspace, and (ii) fractional descriptor linear continuous-time systems are not pointwise degenerated in any nonzero direction for all nonzero initial conditions. The discussion is illustrated with examples of descriptor linear electrical circuits.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 219-223
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of a class of singular linear systems of difference equations. Part 1
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030103.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Rank
Singular difference equations
Opis:
We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
Źródło:
World Scientific News; 2020, 143; 53-66
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of a class of singular linear systems of difference equations. Part 2
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030133.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Moore-Penrose generalized inverse
Singular linear difference systems
Opis:
We extend results of Campbell of the linear systems of differential equations A x ̇+ Bx=f when A and B are rectangular, and results of Kanan of solution of a class of singular linear systems of difference equations A x_(n+1)+ Bx_n=f_n when A and B are square, to such systems of difference equations when A and B are rectangular. Explicit solutions of the last one are derived for several cases. One such is, when the matrix (λA+B) is one-to-one, another case is when such matrix is onto, for a scalar λ∈C. Also, explicit solutions are derived for the case that A is onto, and for the case that B is onto.
Źródło:
World Scientific News; 2020, 143; 127-138
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Drazin inverse of a class of partitioned matrices
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030682.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Partitioned matrix
Rank
Trace of matrix
Opis:
In this work, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@O&A_3 )] with A_1 and A_3 square and singular under the conditions that rank(A_1 )=rank(A_3 )=1, Trace(A_1)≠0 and Trace(A_3)≠0, and then we give the representations of the Drazin inverse for the partitioned EP matrix [■(A_1&A_2@A_3&A_4 )] with A_1 is square and non-singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )]), and [■(A_1&A_2@A_3&A_4 )]=[■(I@P)] A_1 [■(I&Q)] where P=A_3 〖A_1〗^(-1) and Q= 〖A_1〗^(-1) A_2. Also, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@A_3&A_4 )] with A_1 square and singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )])=1, Trace([■(A_1&A_2@A_3&A_4 )])≠0.
Źródło:
World Scientific News; 2020, 139, 2; 173-185
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices
Autorzy:
Kanan, Asmaa M.
Hassan, Khadija
Powiązania:
https://bibliotekanauki.pl/articles/1046563.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Index
Singular differential equations
Opis:
Let A ,B be n×n matrices of complex numbers. Let G a vector-valued function of the real variable t. A and B may both be singular, rank(A) = 1, and the trac of A is not equal zero. The linear system of differential equations Ax^' (t)+Bx(t)=G(t) is studied using the Drazin inverse A^D of A, and a new matrix K∈C^(n×n). In this paper, we obtain a new closed form for the general solution of the differential system when the system is tractable.
Źródło:
World Scientific News; 2019, 137; 229-236
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On controllability and observability of fractional continuous-time linear systems with regular pencils
Autorzy:
Younus, A.
Javaid, I.
Zehra, A.
Powiązania:
https://bibliotekanauki.pl/articles/200494.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
controllability
observability
Gramian matrix
regular pencil
Drazin inverse
sterowalność
obserwowalność
ołówek regularny
odwrotność Drazina
gramian
Opis:
In this paper necessary and sufficient conditions of controllability and observability for solutions of the state equations of fractional continuous time linear systems with regular pencils are proposed. The derivations of the conditions are based on the construction of Gramian matrices.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 3; 297-304
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cayley-Hamilton theorem for Drazin inverse matrix and standard inverse matrices
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201715.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
extension
Cayley-Hamilton theorem
characteristic equation
Drazin inverse
inverse matrix
rozbudowa
twierdzenie Cayleya-Hamiltona
równanie charakterystyczne
macierz odwrotna
odwrotność Drazina
Opis:
The classical Cayley-Hamilton theorem is extended to Drazin inverse matrices and to standard inverse matrices. It is shown that knowing the characteristic polynomial of the singular matrix or nonsingular matrix, it is possible to write the analog Cayley-Hamilton equations for Drazin inverse matrix and for standard inverse matrices.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 4; 793-797
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Drazin inverse matrix method for fractional descriptor discrete-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/201040.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Drazin inverse
descriptor
fractional
discrete-time
linear system solution
odwrotność Drazina
deskryptor
układy dyskretne
system liniowy
Opis:
The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditions for a given set of admissible inputs is established. The proposed method is illustrated by a numerical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 395-399
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of the descriptor Roesser model with the use of the Drazin inverse
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/329922.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Drazin inverse
descriptor
Roesser model
descriptor time
2D linear system
odwrotność Drazina
deskryptor
model Roessera
układ liniowy 2D
Opis:
A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2015, 25, 3; 539-546
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Drazin inverse matrix method for fractional descriptor continuous-time linear systems
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/202103.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
drazin inverse
descriptor
fractional
continuous-time
linear system
solution
Opis:
The Drazin inverse of matrices is applied to find the solutions of the state equations of the fractional descriptor continuous-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 409-412
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positivity and asymptotic stability of descriptor linear systems with regular pencils
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/229772.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
descriptor
Drazin inverse
linear
system
positivity
asymptotic stability
Opis:
The positivity and asymptotic stability of the descriptor linear continuous-time and discrete-time systems with regular pencils are addressed. Necessary and sufficient conditions for the positivity and asymptotic stability of the systems are established using the Drazin inverse matrix approach. Effectiveness of the conditions are demonstrated on numerical examples.
Źródło:
Archives of Control Sciences; 2014, 24, 2; 193-205
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/330552.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Drazin inverse
descriptor
fractional system
discrete-time system
linear system
system ułamkowy
system dyskretno-czasowy
system liniowy
Opis:
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 1; 29-33
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On generalized inverses of singular matrix pencils
Autorzy:
Röbenack, K.
Reinschke, K.
Powiązania:
https://bibliotekanauki.pl/articles/907827.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
macierz
sieć linearna
wskaźnik Kroneckera
matrix pencils
Kronecker indices
Moore-Penrose inverse
Drazin inverse
linear networks
Opis:
Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the multiplicity of poles at zero of the Moore-Penrose inverse and the Drazin inverse of the rational matrix are investigated. We present example networks whose circuit equations yield singular matrix pencils.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 161-172
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 17

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