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1
Content available Stability of convex linear combinations of continuous-time and discrete-time linear systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2023
|
Vol. 33, No. 4
789--799
EN
The asymptotic stability of the convex linear combination of continuous-time and discrete-time linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.
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 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.
4
Content available New stability tests for positive descriptor linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 3
art. no. e140688
EN
The asymptotic stability of positive descriptor continuous-time and discrete-time linear systems is considered. New sufficient conditions for stability of positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of continuous-time and discrete-time linear systems.
5
Content available Exponential decay of transient values in discrete-time positive nonlinear systems
Kaczorek Tadeusz, Ruszewski Andrzej
Archives of Control Sciences
|
2022
|
Vol. 32, No. 3
577--588
EN
The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.
6
Content available A new method for computation of positive realizations of linear discrete-time systems
Kaczorek Tadeusz
Journal of Automation Mobile Robotics and Intelligent Systems
|
2021
|
Vol. 15, No. 1
3--8
EN
A new method for computation of positive realizations of given transfer matrices of linear discretetime linear systems is proposed. Sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by an example.
7
Content available Global stability of positive discrete-time time-varying nonlinear feedback systems
Kaczorek Tadeusz, Sajewski Łukasz
Journal of Automation, Electronics and Electrical Engineering
|
2021
|
Vol. 3, No. 1
17--20
EN
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
8
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.
9
Content available Poles and zeros assignment by state feedbacks in positive linear systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2021
|
Vol. 31, No. 3
593--605
EN
Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n × n system matrix A the sum of n−1 its entries is less than one.
10
Content available New sufficient conditions of global stability of nonlinear positive electrical circuits
Kaczorek Tadeusz
Poznan University of Technology Academic Journals. Electrical Engineering
|
2020
|
No. 103
7--14
EN
The global stability of electrical circuits composed of positive linear parts and nonlinear static element with given characteristic and positive gain feedbacks is investigated. New sufficient conditions for the global stability of this class of nonlinear positive electrical circuits are established. These new stability conditions are demonstrated on simples examples of positive nonlinear electrical circuits.
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 positive standard and fractional nonlinear feedback systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2020
|
Vol. 68, nr 2
285--288
EN
The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.
13
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.
14
Content available Invariant properties of positive linear electrical circuits
Kaczorek Tadeusz
Poznan University of Technology Academic Journals. Electrical Engineering
|
2019
|
No. 97
109--123
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
15
Content available Stability analysis of positive linear systems by decomposition of the state matrices into symmetrical and antisymmetrical parts
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 4
761--768
EN
The stability of positive linear continuous-time and discrete-time systems is analyzed by the use of the decomposition of the state matrices into symmetrical and antisymmetrical parts. It is shown that: 1) The state Metzler matrix of positive continuous-time linear system is Hurwitz if and only if its symmetrical part is Hurwitz; 2) The state matrix of positive linear discrete-time system is Schur if and only if its symmetrical part is Hurwitz. These results are extended to inverse matrices of the state matrices of the positive linear systems.
16
Content available Absolute stability of a class of positive nonlinear continuous-time and discrete-time systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2019
|
Vol. 29, No. 1
157--167
EN
The positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.
17
Content available Absolute stability of a class of nonlinear systems with nonpositive linear parts
Kaczorek Tadeusz
Archives of Control Sciences
|
2019
|
Vol. 29, No. 2
247--258
EN
The positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems with nonpositive linear part are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.
18
Content available remote Normal positive linear systems and electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
|
2018
|
R. 94, nr 6
1--7
EN
The notion of normal positive electrical circuits is introduced and some their specific properties are investigated. New state matrices of positive linear systems and electrical circuits are proposed and their properties are analyzed. It is shown that positive electrical circuits with diagonal state matrices are normal for all values of resistances, inductances and capacitances.
PL
W artykule zaproponowano pojęcie dodatniego obwodu elektrycznego oraz przeanalizowano specjalne własności dodatnich układów i obwodów elektrycznych. Wykazano, że dodatnie obwody elektryczne z diagonalnymi macierzami stanu są zawsze normalne dla wszystkich wartości rezystancji, indukcyjności i pojemności.
19
Content available Normal positive linear systems and electrical circuits
Kaczorek T.
Prace Naukowe Politechniki Śląskiej. Elektryka
|
2018
|
z. 1
7--20
EN
The notion of normal positive electrical circuits is introduced and some their specific properties are investigated. New state matrices of positive linear systems and electrical circuits are proposed and their properties are analyzed. It is shown that positive electrical circuits with diagonal state matrices are normal for all values of resistances, inductances and capacitances.
PL
W artykule zaproponowano pojęcie dodatniego obwodu elektrycznego oraz przeanalizowano specjalne własności dodatnich układów i obwodów elektrycznych. Wykazano, że dodatnie obwody elektryczne z diagonalnymi macierzami stanu są zawsze normalne dla wszystkich wartości rezystancji, indukcyjności i pojemności.
20
Content available Positive continuous – time linear electrical circuit
Piotrowska E.
Poznan University of Technology Academic Journals. Electrical Engineering
|
2018
|
No. 93
299--309
EN
The positive linear continuous-time systems by the use of the Caputo and conformable fractional calculus are analyzed. The conditions for internally positive systems are presented. For the established electrical circuit, a solution fractional order state-space equation was developed for system with Caputo and conformable fractional derivative (CFD) definition.
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