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1
Content available The pointwise completeness and the pointwise degeneracy of fractional descriptor discrete-time linear systems
100%
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
tom 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).
2
Content available remote Asymptotic stability of positive fractional 2D linear systems
100%
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2009
|
tom Vol. 57, nr 3
289-292
3
Content available remote Descriptor fractional linear systems with regular pencils
100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 2
309-315
EN
Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.
4
Content available remote Realization problem for fractional continuous-time systems
100%
Kaczorek T.
Archives of Control Sciences
|
2008
|
tom Vol. 18, no. 1
43-58
EN
The realization problem for positive fractional continuous-time linear systems is addressed. Sufficient conditions for the existence of positive realizations for continuous-time linear systems are established. Procedures for computation of positive fractional realizations for SISO and MIMO continuous-time linear systems are proposed and illustrated by numerical examples.
5
Content available Stability of discrete-time fractional linear systems with delays
100%
Ruszewski A.
Archives of Control Sciences
|
2019
|
tom 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.
6
Content available Stability of fractional positive nonlinear systems
88%
Kaczorek T.
Archives of Control Sciences
|
2015
|
tom Vol. 25, no. 4
491--496
EN
The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
7
Content available Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems
88%
Busłowicz M. , Ruszewski A.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2013
|
tom Vol. 61, nr 4
779--786
EN
In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.
8
Content available Simple analytic conditions for stability of fractional discrete-time linear systems with diagonal state matrix
88%
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2012
|
tom Vol. 60, nr 4
809-814
EN
In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems with a diagonal state matrix are addressed. Standard and positive systems are considered. Simple necessary and sufficient analytic conditions for practical stability and for asymptotic stability are established. The considerations are illustrated by numerical examples.
9
Content available Eigenvalue assignment in fractional descriptor discrete-time linear systems
88%
Kaczorek T. , Borawski K.
Archives of Control Sciences
|
2017
|
tom Vol. 27, no. 1
119--128
EN
The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.
10
Content available Stability analysis of linear continuous-time fractional systems of commensurate order
88%
Busłowicz M.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2009
|
tom Vol. 3, No. 1
12-17
EN
The paper considers the stability problem of linear time-invariant continuous-time systems of fractional commensurate order. It is shown that the system is stable if and only if plot of rational function of fractional order, called as the generalised modified Mikhailov plot, and does not encircle the origin of the complex plane. The considerations are illustrated by numerical examples.
11
Content available Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems
88%
Kaczorek T. , Busłowicz M.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2009
|
tom Vol. 3, No. 1
8-11
EN
A dynamical system described by homogeneous equation is called pointwise complete if every final state can be reached by suitable choice of the initial state. The system which is not pointwise complete is called pointwise degenerated. Definitions and necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of continuous-time linear systems of fractional order, standard and positive, are given. It is shown that: 1) the standard fractional system is always pointwise complete; 2) the positive fractional system is pointwise complete if and only if the state matrix is diagonal.
12
Content available Fractional descriptor observers for fractional descriptor continuous-time linear system
88%
Kaczorek T.
Archives of Control Sciences
|
2014
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tom Vol. 24, no. 1
27--37
EN
Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.
13
Content available Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders
88%
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2012
|
tom Vol. 60, nr 2
279-284
EN
The stability problem of continuous-time linear systems described by the state equation consisting of n subsystems with different fractional orders of derivatives of the state variables has been considered. The methods for asymptotic stability checking have been given. The method proposed in the general case is based on the Argument Principle and it is similar to the modified Mikhailov stability criterion known from the stability theory of natural order systems. The considerations are illustrated by numerical examples.
14
Content available Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits
88%
Kaczorek T.
Journal of Automation, Electronics and Electrical Engineering
|
2023
|
tom 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.
15
Content available The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters
88%
Kaczorek T. , Ruszewski A.
Archives of Control Sciences
|
2024
|
tom Vol. 34, No. 1
83--89
EN
The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.
16
Content available Singular fractional discrete-time linear systems
88%
Kaczorek T.
Control and Cybernetics
|
2011
|
tom Vol. 40, no 3
753-761
EN
A new class of singular fractional linear discretetime systems is introduced. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional linear systems is derived. The considerations are illustrated by numerical examples.
17
Content available Reachability and controllability of positive fractional discrete-time systems with delay
88%
Trzasko W.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2008
|
tom Vol. 2, No. 3
43-47
EN
In the paper the positive fractional discrete-time linear systems with delay described by the state equations are considered. The solution to the state equations is derived using the Z transform. Necessary and sufficient conditions are established for the positivity, reachability and controllability to zero for fractional systems with one delay in state. The considerations are illustrated by an example.
18
Content available remote Responses of standard and fractional linear systems and electrical circuits with derivatives of their inputs
75%
Kaczorek T.
Przegląd Elektrotechniczny
|
2017
|
tom 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.
19
Content available Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks
75%
Kaczorek T.
Archives of Electrical Engineering
|
2014
|
tom Vol. 63, nr 3
321--333
EN
The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils.
20
Content available remote Simple conditions for practical stability of positive fractional discrete-time linear systems
75%
Busłowicz M. , Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 2
263-269
EN
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
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