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1
Content available On the Global stability of fractional feedback nonlinear systems with interval matrices of positive linear parts and application to electrical circuits
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
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2026
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Vol. 36, no. 1
5--11
EN
The global stability of fractional multi-inputs multi-outputs continuous-time nonlinear feedback systems with interval matrices of positive linear parts and application to electrical circuits is investigated. New sufficient conditions for the global stability of fractional nonlinear systems are given. The new stability conditions are applied to nonlinear electrical circuits and demonstrated on a simple example of a fractional nonlinear feedback system with a positive linear part.
2
Content available Invariant properties of positive linear systems with integer and fractional orders
Kaczorek Tadeusz
Archives of Control Sciences
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2026
|
Vol. 36, No. 1
181--194
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear continuous-time systems with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
3
Content available Global Stability of Fractional Feedback Systems with Positive Linear Parts
Kaczorek Tadeusz
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
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2025
|
Vol. 19 No. 1
333--337
EN
The global (absolute) stability of fractional nonlinear systems with negative feedbacks and positive not necessary asymptotically stable linear parts is addressed. It is shown that the coefficients of the transfer matrix of fractional positive asymptotically stable systems are positive. Sufficient conditions for the global stability of the fractional nonlinear systems with positive linear parts are established.
4
Content available Global Stability of Different Fractional Orders Multi Input Multi Output Nonlinear Feedback Systems with Interval Matrices of Positive Linear Parts
Kaczorek Tadeusz, Sajewski Łukasz
TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
|
2025
|
Vol. 19 No. 1
339--344
EN
The global stability of continuous-time fractional orders multi–input multi-output nonlinear feedback systems with interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of these class of positive nonlinear systems are established. A procedure for computation of gain matrix characterizing the class of nonlinear elements is given and illustrated on simple example.
5
Content available Angles between transient values in the linear electrical circuits
Kaczorek Tadeusz
Przegląd Elektrotechniczny
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2025
|
R. 101, nr 6
183--187
EN
The classical definition of the angles between steady values of the voltages and currents in the electrical circuits with constant values of the resistances, inductances and capacitances will be extended to the transient values of the voltages and currents. The theses will be shown on simple electrical circuits with constant resistances, inductances and capacitances. It will be shown that the angles depend on the location of the re sistances, inductances and capacitances of the electrical circuits.
PL
Klasyczna definicja kątów między wartościami ustalonymi napięć i prądów w obwodach elektrycznych o stałych wartościach rezys tancji, indukcyjności i pojemności zostanie rozszerzona na stany przejściowe napięć i prądów. Tezy zostaną przedstawione na prostych obwo dach elektrycznych o stałych wartościach rezystancji, indukcyjności i pojemności. Zostanie pokazane, że kąty zależą od położenia rezystancji, indukcyjności i pojemności obwodów elektrycznych.
6
Content available Positivity and stability of descriptor discrete-time linear systems with interval state matrices
Kaczorek Tadeusz
Journal of Automation Mobile Robotics and Intelligent Systems
|
2025
|
Vol. 19, No. 4
1--6
EN
The positivity and stability of descriptor discrete-time linear systems with interval state matrices are addressed. Necessary and sufficient conditions for the positivity of descriptor discrete-time linear systems are established. The stability of descriptor linear systems with interval state matrices is investigated.
7
Content available Controllability, observability and transfer matrix zeroing of the 2D Roesser model
Kaczorek Tadeusz, Rogowski Krzysztof
Journal of Automation Mobile Robotics and Intelligent Systems
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2025
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Vol. 19, No. 1
1--6
EN
The article considers the fundamental properties of the two-dimensional (2D) system described by the Roesser model. The controllability and observability are analyzed and the sufficient conditions under which the transfer matrix is zero are given. It is shown that if the matrix of the state equation A and B or A and C of the Roesser model has full row rank (respectively, full column rank) then there exists a nonsingular matrix of transformation such that the new pair of new matrices is controllable (observable). The numerical examples are given to show the correctness of the obtained conditions.
8
Content available Discrete-time linear systems with desired poles and zeros of the transfer matrices
Kaczorek Tadeusz, Sajewski Łukasz
International Journal of Applied Mathematics and Computer Science
|
2025
|
Vol. 35, no. 1
59--68
EN
Methods for the design of discrete-time linear systems with desired poles and zeros of their transfer matrices are proposed. Conditions for the existence of the solution to the problem and the procedures for computation of the desired matrices are given. Reduction of the systems with controllable and observable pairs to those with nilpotent matrices is analysed. The procedures are illustrated by simple numerical examples of linear discrete-time systems.
9
Content available Descriptor continuous- and discrete-time linear systems with zero transfer matrices
Kaczorek Tadeusz, Klamka Jerzy, Dzieliński Andrzej
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2025
|
Vol. 73, nr 2
art. no. e152710
EN
In this paper, necessary and sufficient conditions for zeroing of the transfer matrices of descriptor continuous-time and discrete-time linear systems are established. The conditions are illustrated by simple numerical examples of the descriptor continuous-time and discrete-time linear systems. Also some remarks on the systems with delays in control are given.
10
Content available Positive stable linear systems with desired poles and zeros
Sajewski Lukasz, Kaczorek Tadeusz
Archives of Control Sciences
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2025
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Vol. 35, No. 4
729--742
EN
A new method of the decomposition of the fractional descriptor linear continuoustime and discrete-time systems into dynamical and static parts is proposed. Conditions for the decomposition of the fractional descriptor linear systems are established and procedures for compositions of the matrices of dynamical and static parts are given. The procedures are illustrated by numerical examples.
11
Content available Observers for unobservable linear systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2025
|
Vol. 35, No. 1
145--154
EN
Observers for unobservable linear systems ẋ = 𝐴𝑥 + 𝐵𝑢, 𝑦 = 𝐶𝑥, 𝑥 = 𝑥(𝑡) ∈ ℜ𝑛, 𝑢 = 𝑢(𝑡) ∈ ℜm, 𝑦 = 𝑦(𝑡) ∈ ℜp are proposed. It is shown that there exist full-order and reduced-order observers for systems satisfying the condition rank [𝐴 𝐶] = 𝑛. Procedures for computation of the matrices of the observers are given and illustrated by numerical examples.
12
Content available Global stability of nonlinear systems with positive linear parts and positive dynamical feedbacks
Kaczorek Tadeusz
Archives of Control Sciences
|
2025
|
Vol. 35, No. 2
251--263
EN
The global stability of nonlinear continuous-time standard and fractional order with linear dynamical positive feedback systems and of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Procedures for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple examples.
13
Content available Transformations of the discrete-time linear systems to the positive asymptotically stable forms
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2024
|
Vol. 6, No. 2
23--34
EN
New approaches to the transformations of the discrete-time linear systems to their positive asymptotically stable canonical controllable (observable) forms is proposed. It is shown that if the matrix A of the system is nonsingular then the desired transformation matrix can be chosen in block diagonal form. Procedures for computation of the transformation matrices are proposed and illustrated by simple numerical examples.
14
Content available Transfer matrices with positive coefficients of descriptor linear systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
|
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.
15
Content available A new approach to the stabilization problem of linear systems
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2024
|
Vol. 6, No. 2
7--22
EN
A new approach for the stabilization of the linear continuous-time and discrete-time systems is proposed. The desired asymptotically stable state matrices of the linear systems are obtained by pre-multiplication and post-multiplication of the system matrix by suitable square matrix. Procedures for computation of the matrices are given and illustrated by simple numerical examples.
16
Content available Transformations of linear standard systems to positive asymptotically stable linear ones
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2024
|
Vol. 34, no. 3
341--348
EN
New approaches to transformations of linear continuous-time systems to their positive asymptotically stable canonical controllable (observable) forms are proposed. It is shown that, if the system matrix is nonsingular, then the desired transformation matrix can be chosen in block diagonal form. Procedures for the computation of the transformation matrices are proposed and illustrated with simple numerical examples.
17
Content available Exponential decay of transient values in positive nonlinear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2024
|
Vol. 72, nr 5
art. no. e151050
EN
The exponential decay of transient values in nonlinear continuous-time standard and fractional orders with linear dynamical positive feedback systems and of positive linear parts is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. Procedures for the computation of gains characterizing the class of nonlinear elements are given and illustrated in simple examples.
18
Content available The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters
Kaczorek Tadeusz, Ruszewski Andrzej
Archives of Control Sciences
|
2024
|
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.
19
Content available Analysis of the fractional descriptor linear systems by the decomposition into the dynamical and static parts
Kaczorek Tadeusz, Sajewski Lukasz
Archives of Control Sciences
|
2024
|
Vol. 34, No. 4
743--753
EN
A new method of the decomposition of the fractional descriptor linear continuoustime and discrete-time systems into dynamical and static parts is proposed. Conditions for the decomposition of the fractional descriptor linear systems are established and procedures for compositions of the matrices of dynamical and static parts are given. The procedures are illustrated by numerical examples.
20
Content available Controllability and observability of the descriptor linear systems reduced to the standard ones by feedbacks
Kaczorek Tadeusz, Klamka Jerzy, Dzieliński Andrzej
Acta Mechanica et Automatica
|
2024
|
Vol. 18, no. 1
119--122
EN
In this paper, a new method for the reduction of the descriptor linear systems to standards ones is presented and verified. The method uses a state and/or state derivative feedback of output and output derivative feedback in order to transform the descriptor system into a standard one. The controllability and observability properties of the original descriptor as well as transformed standard systems are proved. Simple numerical examples illustrate the theorems introduced.
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