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  1. 20 Bulletin of the Polish Academy of Sciences. Technical Sciences
  2. 15 Archives of Control Sciences
  3. 5 Poznan University of Technology Academic Journals. Electrical Engineering
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  1. 59 Kaczorek T.
  2. 10 Kaczorek Tadeusz
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1
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.
2
Content available Analysis of the pointwise completeness and the pointwise degeneracy of the standard and fractional descriptor linear systems and electrical circuits
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2023
|
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.
3
Content available Observers of fractional linear continuous-time systems
Kaczorek Tadeusz
Archives of Control Sciences
|
2022
|
Vol. 32, No. 1
73--84
EN
The concepts of full-order and reduced-order observers are extended to the fractional linear continuous-time systems. Necessary and sufficient conditions for the existence of the observers for fractional linear systems are established. Procedures for designing of the observers are given and illustrated by examples.
4
Content available Structurally R-controllable and structurally R-observable descriptor linear electrical circuits
Kaczorek Tadeusz, Borawski Kamil
Journal of Automation Mobile Robotics and Intelligent Systems
|
2021
|
Vol. 15, No. 3
81--86
EN
Structurally R-controllable and structurally R-observable descriptor linear electrical circuits are investigated. Sufficient conditions are given under which the R- controllability and R-observability of descriptor linear electrical circuits are independent of their parameters.
5
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.
6
Content available Application of the Lagrange-Sylvester formula to computation of the solution to state equations of fractional linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2021
|
Vol. 69, nr 2
art. no. e136729
EN
The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems. The solutions are given as finite sums with their numbers of components equal to the degrees of the minimal characteristics polynomials of state matrices of the systems. Procedures for computations of the solutions are given and illustrated by numerical examples of continuous-time and discrete-time fractional linear systems.
7
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.
8
Content available Linear megastructures. An eccentric pursuit in tackling urban sustainability challenges
Tufek-Memisevic Tijana, Stachura Ewa
Środowisko Mieszkaniowe
|
2019
|
nr 29
54--59
EN
Linear megastructures, apart from megastructures in general, are one of several types of concepts in context of linear urban development. The term refers to various compact architectural, infrastructural and transportation plans in linear form. With their daunting massive scale these concepts are often attributed to utopian attempts of pursuing an ideal city and therefore doomed to remain unrealized. This paper examines several models created throughout the course of history in terms of their emergence motivation, socio-economic circumstances and relation to urban sustainability. Through the analysis, it is argued that linear megastructures are often unjustly rejected without acknowledgement of their underlying beneficial features in terms of mitigating challenges to sustainable urban development.
9
Content available remote Generalized Frobenius matrices and angles between them in analysis of linear electrical circuits
Kaczorek Tadeusz
Przegląd Elektrotechniczny
|
2019
|
R. 95, nr 9
13--19
EN
Generalized Frobenius matrices and their inverses are applied in analysis of the linear electrical circuits. The basic properties of generalized Frobenius matrices are analyzed. It is shown that if the state matrix of electrical circuit has generalized Frobenius form then its inverse system matrix has also generalized Frobenius form. The notion of an angle between state matrices of linear electrical circuits is proposed and its basic properties are investigated.
PL
Zaproponowane w tej pracy uogólnione macierze Frobeniusa oraz ich odwrotności zostały zastosowane w analizie liniowych obwodów elektrycznych. Zostały zbadane podstawowe własności tych macierzy. Wykazano między innymi, że macierze odwrotne uogólnionych macierzy Frobeniusa mają również postać uogólnionych macierzy Frobeniusa .Wprowadzono pojęcie kąta między macierzami stanu liniowych obwodów elektrycznych oraz zbadano ich podstawowe własności.
10
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.
11
Content available Independence of the controllability and observability of resistances in linear electrical circuits
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2019
|
Vol. 1, No. 1
9--15
EN
Sufficient conditions are given under which the controllability and observability of linear electrical circuits is independent of their resistances. In some particular cases the observability depends only on the capacitances or inductances of the electrical circuits.
12
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.
13
Content available Positivity of fractional descriptor linear continuous-time systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2019
|
Vol. 67, nr 2
229--233
EN
The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.
14
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.
15
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.
16
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.
17
Content available Analysis of the positivity and stability of linear electrical circuits with state-feedbacks
Kaczorek T.
Poznan University of Technology Academic Journals. Electrical Engineering
|
2018
|
No. 93
21--36
EN
The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.
18
Content available CMOS ECCCII with Linear Tune of Rx and Its Application to Current-Mode Multiplier
Sakul C.
International Journal of Electronics and Telecommunications
|
2018
|
Vol. 64, No. 3
385--390
EN
In this paper, the second-generation CMOS currentcontrolled-current-conveyor based on differential pair of operational transconductance amplifier has been researched and presented. Since the major improvement of its parasitic resistance at x-port can be linearly controlled by an input bias current, the proposed building block is then called “The Second-Generation Electronically-tunable Current-controlled Current Conveyor” (ECCCI). The applications are demonstrated in form of both 2 quadrant and 4 quadrant current-mode signal multiplier circuits. Characteristics of the proposed ECCCII and its application are simulated by the PSPICE program from which the results are proved to be in agreement with the theory.
19
Content available Stability of interval positive continuous-time linear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 1
31--35
EN
It is shown that the convex linear combination of the Hurwitz polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive interval linear systems. It is also shown that the interval positive linear system described by state equation x ̇ = Ax, A ϵ ℜn×n, A1 ≥ A ≤ A2 is asymptotically stable if and only if the matrices Ak = 1, 2 are Hurwitz Metzler matrices.
20
Content available A new method for determination of positive realizations of linear continuous-time systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2018
|
Vol. 66, nr 5
605--611
EN
A new method for determination of positive realizations of given transfer matrices of linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are presented. A procedure for computation of the positive realizations is proposed and illustrated by an example.
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