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  1. Електронний науковий архів Науково-технічної бібліотеки Національного університету "Львівська політехніка"
  2. Електронний архів Науково-технічної бібліотеки
  3. Вісники та науково-технічні збірники, журнали
  4. Computational Problems of Electrical Engineering
  5. Computational Problems Of Electrical Engineering. – 2018 – Vol. 8, No. 1

putin IS MURDERER

Please use this identifier to cite or link to this item: https://oldena.lpnu.ua/handle/ntb/46075
Title: Positivityand stability of descriptor linear systems with interval state matrices
Other Titles: Позитивність та стійкість дескрипторних лінійних систем з інтервальними матрицями стану
Authors: Качорек, Тадеуш
Kaczorek, Tadeusz
Affiliation: Bialystok University of Technology
Bibliographic description (Ukraine): Kaczorek T. Positivityand stability of descriptor linear systems with interval state matrices / Tadeusz Kaczorek // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 8. — No 1. — P. 7–17.
Bibliographic description (International): Kaczorek T. Positivityand stability of descriptor linear systems with interval state matrices / Tadeusz Kaczorek // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 8. — No 1. — P. 7–17.
Is part of: Computational Problems of Electrical Engineering, 1 (8), 2018
Issue: 1
Issue Date: 1-Feb-2018
Publisher: Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
Keywords: interval
positive
descriptor
linear
system
stability
extension
Kharitonov theorem
Number of pages: 11
Page range: 7-17
Start page: 7
End page: 17
Abstract: Досліджено позитивність та асимптотичну стійкість дескрипторних лінійних часово неперервних та дискретних систем з інтервальними матрицями стану та інтервальними поліномами. Встановлено необхідні та достатні умови для позитивності лінійних часово неперервних та дискретних систем. Показано, що опукла лінійна комбінація поліномів позитивних лінійних систем також є поліномом Гурвіца. Поширено теорему Харітонова на позитивні дескрипторні лінійні системи з інтервальними матрицями стану. Також встановлено необхідні та достатні умови для асимптотичної стійкості дескрипторних позитивних лінійних систем. Розглянуті припущення проілюс- тровано за допомогою числових прикладів.
The positivity and asymptotic stability of descriptor linear continuous-time and discrete-time systems with interval state matrices and interval polynomials are investigated. Necessary and sufficient conditions for the positivity of descriptor continuoustime and discrete-time linear systems are established. It is shown that the convex linear combination of polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive descriptor linear systems with interval state matrices. Necessary and sufficient conditions for the asy mptotic stability of descriptor positive linear systems have been also established. The considerations have been illustrated by numerical examples.
URI: https://ena.lpnu.ua/handle/ntb/46075
Copyright owner: © Національний університет “Львівська політехніка”, 2018
© Kaczorek T., 2018
URL for reference material: https://doi.org/10.1515/ijnsns-2017-0049
References (Ukraine): 1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
2. M. Busłowicz, “Stability of linear continuous-time fractional order systems with delays of the retarded type“, Bull. Pol. Acad. Sci. Tech., vol. 56, no. 4, pp. 319–324, 2008.
3. M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different
4. M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, pp. 263–169, 2009.
5. L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J.Wiley, New York, 2000.
6. T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Acad. Sci. Tech., vol. 64, no. 3, pp. 491–494, 2016.
7. T. Kaczorek, “Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems”, Computational Problems of Electrical Engineering, vol. 5, no. 1, pp. 11–16, 2015.
8. T. Kaczorek, “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci., vol. 23, no. 1, 29–34, 2013.
9. T. Kaczorek, “Descriptor positive discrete-time and continuous-time nonlinear systems”, Proc. of SPIE, vol. 9290, 2014.
10. T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci., vol. 18, no. 2, pp. 223–228, 2008,.
11. T. Kaczorek, Positive 1D and 2D Systems, Springer- Verlag, London, 2002.
12. T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, pp. 453–458, 2010.
13. T. Kaczorek, “Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems”, Int. J. of Nonlinear Sciences and Num. Simul., 2018 (in press) DOI: https://doi.org/10.1515/ijnsns-2017-0049.
14. T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, pp. 1203–1210, 2011.
15. T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, pp. 9–12, 2012.
16. T. Kaczorek, “Positive singular discrete-time linear systems”, Bull. Pol. Acad. Sci. Tech., vol. 45, no. 4, pp. 619-631, 1997.
17. T. Kaczorek, “Positivity and stability of discretetime nonlinear systems”, IEEE 2nd International Conference on Cybernetics, pp. 156–159, 2015.
18. T. Kaczorek, “Stability of fractional positive nonlinear systems”, Archives of Control Sciences, vol. 25, no. 4, pp. 491–496, 2015.
19. T. Kaczorek, “Stability of interval positive continuoustime linear systems”, Bull. Pol. Acad. Sci. Techn., vol. 66, no. 1, 2018.
20. T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
21. V. L. Kharitonov, “Asymptotic stability of an equilibrium position of a family of systems of differential equations, Differentsialnye uravneniya, vol. 14, pp. 2086–2088, 1978.
22. L. Sajewski, “Descriptor fractional discrete-time linear system and its solution – comparison of three different methods”, Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems and Computing, vol. 440, pp. 37–50, 2016.
23. L. Sajewski, “Descriptor fractional discrete-time linear system with two different fractional orders and its solution”, Bull. Pol. Acad. Sci. Tech., vol. 64, no. 1, pp. 15–20, 2016.
24. H. Zhang, D. Xie, H. Zhang and G. Wang, “Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach”, ISA Transactions, vol. 53, pp. 1081–1086, 2014.
25. J. Zhang, Z. Han, H. Wu, and J. Hung, “Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching”, Circuits Syst. Signal Process., vol. 33, pp. 71–95, 2014.
26. W. Xiang-Jun, W. Zheng-Mao, and L. Jun-Guo, “Stability analysis of a class of nonlinear fractionalorder systems”, IEEE Trans. Circuits and Systems-II, Express Briefs, vol. 55, no. 11, pp. 1178–1182, 2008
References (International): 1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
2. M. Busłowicz, "Stability of linear continuous-time fractional order systems with delays of the retarded type", Bull. Pol. Acad. Sci. Tech., vol. 56, no. 4, pp. 319–324, 2008.
3. M. Busłowicz, "Stability analysis of continuous-time linear systems consisting of n subsystems with different
4. M. Busłowicz and T. Kaczorek, "Simple conditions for practical stability of positive fractional discrete-time linear systems", Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, pp. 263–169, 2009.
5. L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J.Wiley, New York, 2000.
6. T. Kaczorek, "Analysis of positivity and stability of fractional discrete-time nonlinear systems", Bull. Pol. Acad. Sci. Tech., vol. 64, no. 3, pp. 491–494, 2016.
7. T. Kaczorek, "Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems", Computational Problems of Electrical Engineering, vol. 5, no. 1, pp. 11–16, 2015.
8. T. Kaczorek, "Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils", Int. J. Appl. Math. Comput. Sci., vol. 23, no. 1, 29–34, 2013.
9. T. Kaczorek, "Descriptor positive discrete-time and continuous-time nonlinear systems", Proc. of SPIE, vol. 9290, 2014.
10. T. Kaczorek, "Fractional positive continuous-time linear systems and their reachability", Int. J. Appl. Math. Comput. Sci., vol. 18, no. 2, pp. 223–228, 2008,.
11. T. Kaczorek, Positive 1D and 2D Systems, Springer- Verlag, London, 2002.
12. T. Kaczorek, "Positive linear systems with different fractional orders", Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, pp. 453–458, 2010.
13. T. Kaczorek, "Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems", Int. J. of Nonlinear Sciences and Num. Simul., 2018 (in press) DOI: https://doi.org/10.1515/ijnsns-2017-0049.
14. T. Kaczorek, "Positive linear systems consisting of n subsystems with different fractional orders", IEEE Trans. on Circuits and Systems, vol. 58, no. 7, pp. 1203–1210, 2011.
15. T. Kaczorek, "Positive fractional continuous-time linear systems with singular pencils", Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, pp. 9–12, 2012.
16. T. Kaczorek, "Positive singular discrete-time linear systems", Bull. Pol. Acad. Sci. Tech., vol. 45, no. 4, pp. 619-631, 1997.
17. T. Kaczorek, "Positivity and stability of discretetime nonlinear systems", IEEE 2nd International Conference on Cybernetics, pp. 156–159, 2015.
18. T. Kaczorek, "Stability of fractional positive nonlinear systems", Archives of Control Sciences, vol. 25, no. 4, pp. 491–496, 2015.
19. T. Kaczorek, "Stability of interval positive continuoustime linear systems", Bull. Pol. Acad. Sci. Techn., vol. 66, no. 1, 2018.
20. T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
21. V. L. Kharitonov, "Asymptotic stability of an equilibrium position of a family of systems of differential equations, Differentsialnye uravneniya, vol. 14, pp. 2086–2088, 1978.
22. L. Sajewski, "Descriptor fractional discrete-time linear system and its solution – comparison of three different methods", Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems and Computing, vol. 440, pp. 37–50, 2016.
23. L. Sajewski, "Descriptor fractional discrete-time linear system with two different fractional orders and its solution", Bull. Pol. Acad. Sci. Tech., vol. 64, no. 1, pp. 15–20, 2016.
24. H. Zhang, D. Xie, H. Zhang and G. Wang, "Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach", ISA Transactions, vol. 53, pp. 1081–1086, 2014.
25. J. Zhang, Z. Han, H. Wu, and J. Hung, "Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching", Circuits Syst. Signal Process., vol. 33, pp. 71–95, 2014.
26. W. Xiang-Jun, W. Zheng-Mao, and L. Jun-Guo, "Stability analysis of a class of nonlinear fractionalorder systems", IEEE Trans. Circuits and Systems-II, Express Briefs, vol. 55, no. 11, pp. 1178–1182, 2008
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