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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 2
277-283
EN
Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
2
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Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders

100%
Sajewski Ł.
International Journal of Applied Mathematics and Computer Science
|
2017
|
tom 27
|
nr 1
33-41
EN
Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
3
Content available remote

Minimum energy control of fractional descriptor positive discrete-time linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
735-743
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
4
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Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
|
nr 3
501-506
EN
Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
5
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Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 2
217-221
EN
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
6
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Positivity and stability of fractional descriptor time-varying discrete-time linear systems

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 1
5-13
EN
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
7
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative

88%
Kaczorek T., Borawski K.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
533-541
EN
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
8
Content available remote

Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 1
29-33
EN
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.
9
Content available remote

Singular fractional linear systems and electrical circuits

75%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 2
379-384
EN
A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.
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