Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/55978
Title: Angles Between Matrices and Between Polynomials in Fractional Linear Systems and Electrical Circuits
Other Titles: Кути між матрицями та між поліномами в дробових лінійних системах та електричних колах
Authors: Качорек, Тадеуш
Kaczorek, Tadeusz
Affiliation: Bialystok University of Technology
Bibliographic description (Ukraine): Kaczorek T. Angles Between Matrices and Between Polynomials in Fractional Linear Systems and Electrical Circuits / Tadeusz Kaczorek // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 1–10.
Bibliographic description (International): Kaczorek T. Angles Between Matrices and Between Polynomials in Fractional Linear Systems and Electrical Circuits / Tadeusz Kaczorek // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 1–10.
Is part of: Computational Problems of Electrical Engineering, 1 (10), 2020
Issue: 1
Issue Date: 24-Feb-2020
Publisher: Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
Keywords: angle between matrices
polynomials
matrix function
linear
electrical circuit
Number of pages: 10
Page range: 1-10
Start page: 1
End page: 10
Abstract: Сформульовано поняття кутів між матрицями та між поліномами дробових лінійних систем та електричних кіл. Під час аналізу кутів між матрицями стану дробових лінійних систем засновано добуток Адамара з двох матриць. Розглянуто також кути між матрицями та їх функції. Досліджено кути між симетричною й несиметричною частинами матриць. Проаналізовано кути між поліномами передатних матриць дробових лінійних систем та встановлено їхні деякі нові властивості.
The notions of angles between matrices and between polynomials of fractional linear systems and electrical circuits are proposed. In analysis of angles between state matrices of fractional linear systems the Hadamard product of two matrices is applied. The angles between matrices and their functions are also addressed. The angles between symmetrical and asymmetrical part of matrices are investigated. The angles between polynomials of transfer matrices of fractional linear systems are analyzed and some new properties are established.
URI: http://ena.lp.edu.ua:8080/handle/ntb/55978
Copyright owner: © Національний університет “Львівська політехніка”, 2020
References (Ukraine): [1] M. Ait Rami and F. Tadeo, “Controller Synthesis for Positive Linear Systems With Bounded Controls”, IEEE Transactions on Circuits and Systems, vol. 54, no. 2, pp. 151–155, 2007.
[2] S. Domek and P. Dworakm Theoretical Developments and Aplications of Non-Integer Order Systems, Springer 2016.
[3] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
[4] F. R. Gantmacher, The Theory of Matrices. Chelsea 1974.
[5] T. Kaczorek,: “A class of positive and stable timevarying electrical circuits. Electrical Review”, vol. 91, no. 5, 2015, 121–124.
[6] T. Kaczorek, “Angles between matrices and between polynomials in analysis of electrical circuits”, Proceedings of SPIE, Bellingham WA, USA, Art. vol. 8903, no 3903–35.
[7] T. Kaczorek, “Normal positive electrical circuits”, IET Circuits Theory and Applications, vol. 9, no. 5, pp. 691–699, 2015.
[8] T. Kaczorek, Positive 1D and 2D Systems. SpringerVerlag. London, 2002.
[9] T. Kaczorek, “Positive electrical circuits and their reachability”, Archives of Electrical Engineering, vol. 60, no. 3, pp. 283–301, 2011.
[10] T. Kaczorek Positive fractional linear electrical circuits, Proceedings of SPIE, vol. 8903, Bellingham WA, USA, Art. No 3903–35.
[11] T. Kaczorek, Positive and stable electrical circuits with state matrices, Archives of Electrical Engineering, vol. 67, no. 3, pp. 563–578, 2018.
[12] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
[13] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa,1998 (in Polish).
[14] T. Kaczorek and K. Borawski, “Stability of continuous-time and discrete-time linear systems with inverse state matrices”, Measurement Automation Monitoring, vol. 62, no. 4, pp. 132–135, 2016.
[15] T. Kaczorek and K. Rogowski, “Fractional Linear Systems and Electrical Circuits”, Studies in Systems, Decision and Control, vol. 13, Springer, 2015.
[16] T. Kaczorek and L. Sajewski, “Transfer matrices with positive coefficients for standard and fractional positive linear systems”, in Proc. MMAR, Międzyzdroje 2018, http:/ieeeexplore.ieee.org.
[17] K.J.L atawiec, M. Lukaniszyn and R. Stanisławski, Advances in Modelling and Control of Non-integer Order Systems, Springer 2015.
[18] A. B. Malinowska, D. Mozyrska and L. Sajewski Advances in Non-Integer Order Calculus and Its Applications, Springer 2020.
[19] P. Ostalczyk, Discrete Fractional Calculus, World Scientific, 2016.
References (International): [1] M. Ait Rami and F. Tadeo, "Controller Synthesis for Positive Linear Systems With Bounded Controls", IEEE Transactions on Circuits and Systems, vol. 54, no. 2, pp. 151–155, 2007.
[2] S. Domek and P. Dworakm Theoretical Developments and Aplications of Non-Integer Order Systems, Springer 2016.
[3] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
[4] F. R. Gantmacher, The Theory of Matrices. Chelsea 1974.
[5] T. Kaczorek,: "A class of positive and stable timevarying electrical circuits. Electrical Review", vol. 91, no. 5, 2015, 121–124.
[6] T. Kaczorek, "Angles between matrices and between polynomials in analysis of electrical circuits", Proceedings of SPIE, Bellingham WA, USA, Art. vol. 8903, no 3903–35.
[7] T. Kaczorek, "Normal positive electrical circuits", IET Circuits Theory and Applications, vol. 9, no. 5, pp. 691–699, 2015.
[8] T. Kaczorek, Positive 1D and 2D Systems. SpringerVerlag. London, 2002.
[9] T. Kaczorek, "Positive electrical circuits and their reachability", Archives of Electrical Engineering, vol. 60, no. 3, pp. 283–301, 2011.
[10] T. Kaczorek Positive fractional linear electrical circuits, Proceedings of SPIE, vol. 8903, Bellingham WA, USA, Art. No 3903–35.
[11] T. Kaczorek, Positive and stable electrical circuits with state matrices, Archives of Electrical Engineering, vol. 67, no. 3, pp. 563–578, 2018.
[12] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
[13] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa,1998 (in Polish).
[14] T. Kaczorek and K. Borawski, "Stability of continuous-time and discrete-time linear systems with inverse state matrices", Measurement Automation Monitoring, vol. 62, no. 4, pp. 132–135, 2016.
[15] T. Kaczorek and K. Rogowski, "Fractional Linear Systems and Electrical Circuits", Studies in Systems, Decision and Control, vol. 13, Springer, 2015.
[16] T. Kaczorek and L. Sajewski, "Transfer matrices with positive coefficients for standard and fractional positive linear systems", in Proc. MMAR, Międzyzdroje 2018, http:/ieeeexplore.ieee.org.
[17] K.J.L atawiec, M. Lukaniszyn and R. Stanisławski, Advances in Modelling and Control of Non-integer Order Systems, Springer 2015.
[18] A. B. Malinowska, D. Mozyrska and L. Sajewski Advances in Non-Integer Order Calculus and Its Applications, Springer 2020.
[19] P. Ostalczyk, Discrete Fractional Calculus, World Scientific, 2016.
Content type: Article
Appears in Collections:Computational Problems Of Electrical Engineering. – 2020 – Vol. 10, No. 1



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