Positivityand stability of descriptor linear systems with interval state matrices

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dc.citation.epage17
dc.citation.issue1
dc.citation.spage7
dc.contributor.affiliationBialystok University of Technology
dc.contributor.authorКачорек, Тадеуш
dc.contributor.authorKaczorek, Tadeusz
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-26T10:58:34Z
dc.date.available2020-02-26T10:58:34Z
dc.date.created2018-02-01
dc.date.issued2018-02-01
dc.description.abstractДосліджено 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.
dc.description.abstractThe 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.
dc.format.extent7-17
dc.format.pages11
dc.identifier.citationKaczorek 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.
dc.identifier.citationenKaczorek 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.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/46075
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofComputational Problems of Electrical Engineering, 1 (8), 2018
dc.relation.references1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
dc.relation.references2. 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.
dc.relation.references3. M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different
dc.relation.references4. 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.
dc.relation.references5. L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J.Wiley, New York, 2000.
dc.relation.references6. 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.
dc.relation.references7. 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.
dc.relation.references8. 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.
dc.relation.references9. T. Kaczorek, “Descriptor positive discrete-time and continuous-time nonlinear systems”, Proc. of SPIE, vol. 9290, 2014.
dc.relation.references10. 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,.
dc.relation.references11. T. Kaczorek, Positive 1D and 2D Systems, Springer- Verlag, London, 2002.
dc.relation.references12. T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, pp. 453–458, 2010.
dc.relation.references13. 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.
dc.relation.references14. 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.
dc.relation.references15. T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, pp. 9–12, 2012.
dc.relation.references16. T. Kaczorek, “Positive singular discrete-time linear systems”, Bull. Pol. Acad. Sci. Tech., vol. 45, no. 4, pp. 619-631, 1997.
dc.relation.references17. T. Kaczorek, “Positivity and stability of discretetime nonlinear systems”, IEEE 2nd International Conference on Cybernetics, pp. 156–159, 2015.
dc.relation.references18. T. Kaczorek, “Stability of fractional positive nonlinear systems”, Archives of Control Sciences, vol. 25, no. 4, pp. 491–496, 2015.
dc.relation.references19. T. Kaczorek, “Stability of interval positive continuoustime linear systems”, Bull. Pol. Acad. Sci. Techn., vol. 66, no. 1, 2018.
dc.relation.references20. T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
dc.relation.references21. 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.
dc.relation.references22. 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.
dc.relation.references23. 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.
dc.relation.references24. 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.
dc.relation.references25. 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.
dc.relation.references26. 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
dc.relation.referencesen1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
dc.relation.referencesen2. 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.
dc.relation.referencesen3. M. Busłowicz, "Stability analysis of continuous-time linear systems consisting of n subsystems with different
dc.relation.referencesen4. 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.
dc.relation.referencesen5. L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J.Wiley, New York, 2000.
dc.relation.referencesen6. 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.
dc.relation.referencesen7. 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.
dc.relation.referencesen8. 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.
dc.relation.referencesen9. T. Kaczorek, "Descriptor positive discrete-time and continuous-time nonlinear systems", Proc. of SPIE, vol. 9290, 2014.
dc.relation.referencesen10. 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,.
dc.relation.referencesen11. T. Kaczorek, Positive 1D and 2D Systems, Springer- Verlag, London, 2002.
dc.relation.referencesen12. T. Kaczorek, "Positive linear systems with different fractional orders", Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, pp. 453–458, 2010.
dc.relation.referencesen13. 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.
dc.relation.referencesen14. 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.
dc.relation.referencesen15. T. Kaczorek, "Positive fractional continuous-time linear systems with singular pencils", Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, pp. 9–12, 2012.
dc.relation.referencesen16. T. Kaczorek, "Positive singular discrete-time linear systems", Bull. Pol. Acad. Sci. Tech., vol. 45, no. 4, pp. 619-631, 1997.
dc.relation.referencesen17. T. Kaczorek, "Positivity and stability of discretetime nonlinear systems", IEEE 2nd International Conference on Cybernetics, pp. 156–159, 2015.
dc.relation.referencesen18. T. Kaczorek, "Stability of fractional positive nonlinear systems", Archives of Control Sciences, vol. 25, no. 4, pp. 491–496, 2015.
dc.relation.referencesen19. T. Kaczorek, "Stability of interval positive continuoustime linear systems", Bull. Pol. Acad. Sci. Techn., vol. 66, no. 1, 2018.
dc.relation.referencesen20. T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
dc.relation.referencesen21. 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.
dc.relation.referencesen22. 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.
dc.relation.referencesen23. 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.
dc.relation.referencesen24. 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.
dc.relation.referencesen25. 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.
dc.relation.referencesen26. 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
dc.relation.urihttps://doi.org/10.1515/ijnsns-2017-0049
dc.rights.holder© Національний університет “Львівська політехніка”, 2018
dc.rights.holder© Kaczorek T., 2018
dc.subjectinterval
dc.subjectpositive
dc.subjectdescriptor
dc.subjectlinear
dc.subjectsystem
dc.subjectstability
dc.subjectextension
dc.subjectKharitonov theorem
dc.titlePositivityand stability of descriptor linear systems with interval state matrices
dc.title.alternativeПозитивність та стійкість дескрипторних лінійних систем з інтервальними матрицями стану
dc.typeArticle

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