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Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems

Yıl 2022, Cilt: 5 Sayı: 1, 10 - 14, 15.03.2022
https://doi.org/10.32323/ujma.1055172

Öz

In this paper, the problem of dwell time for the Hurwitz stability of switched linear systems is considered. Dwell time is determined based on the solution of Lyapunov matrix equation for the Hurwitz stability of switched linear differential systems. A numerical example illustrating the efficiency of theorem has been given.

Kaynakça

  • [1] S. Solmaz, R. Shorten, K. Wulff, F. O’Cairbre, A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control, Automatica, 44(9) (2008), 2358-2363.
  • [2] A. Balluchi, M. D. Benedetto, C. Pinello, C. Rossi, A. Sangiovanni-Vincentelli, Cut-off in Engine Control, A Hybrid System Approach, Proceedings of the 36th IEEE Conference on Decision and Control, (1997), 4720–4725.
  • [3] B. E. Bishop, M. W. Spong, Control of Redundant Manipulators Using Logic-Based Switching, Proceedings of the 36th IEEE Conference on Decision and Control, (1998), 16–18.
  • [4] W. Zhang, M. S. Branicky, S. M. Phillips, Stability of Networked Control Systems, IEEE Control Systems Magazine, 21(1) (1998), 84–99.
  • [5] D. Z. Chen, Y. J. Guo, Advances on Switched Systems, Control Theory and Applications, 22(6) (2005), 954–960.
  • [6] H. Lin and P. J. Antsaklis, Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, IEEE Trans. Automat. Contr., 54(2) (2009), 308-322.
  • [7] J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, Proc. of the 38th Conf. on Decision and Control, (1999), 2655–2660.
  • [8] O¨ . Karabacak, Dwell time and average dwell time methods based on the cycle ratio of the switching graph, Systems Control Lett., 62(2013), 1032–1037.
  • [9] A. Ya. Bulgakov, An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients, Siberian Math. J., 21(1980), 339–347.
  • [10] A. Ya. Bulgakov, Matrix Computations with Guaranteed Accuracy in Stability Theory, Selc¸uk University, The Research Center of Applied Mathematics, Konya, 1995.
  • [11] S. K. Godunov, Ordinary Differential Equations with Constant Coefficients, Translations of Mathematical Monographs, 169, American Mathematical Society, Providence, RI, 1997.
  • [12] H. Bulgak, Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability, in Error Control and Adaptivity in Scientific Computing, eds. H. Bulgak and C. Zenger, NATO Science Series, Series C: Mathematical and Physical Sciences, 536 (Kluwer Academic Publishers, Dordrecht, 1999), 95–124.
  • [13] A. Duman, K. Aydın, Sensitivity of Hurwitz stability of linear differential equation systems with constant coefficients, Int. J. Geom. Methods Mod. Phys., 14 (2017), 1750084.
  • [14] S. K. Godunov, Modern Aspects of Linear Algebra, Translations of Mathematical Monographs, 175, American Mathematical Society, Providence, RI, 1998.
  • [15] Y. M. Nechepurenko, Bounds for the matrix exponential based on the Lyapunov equation and limits of yhe ,Hausdorff set, Computational Mathematics and Mathematical Physics, 42(2) (2002), 125-134.
Yıl 2022, Cilt: 5 Sayı: 1, 10 - 14, 15.03.2022
https://doi.org/10.32323/ujma.1055172

Öz

Kaynakça

  • [1] S. Solmaz, R. Shorten, K. Wulff, F. O’Cairbre, A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control, Automatica, 44(9) (2008), 2358-2363.
  • [2] A. Balluchi, M. D. Benedetto, C. Pinello, C. Rossi, A. Sangiovanni-Vincentelli, Cut-off in Engine Control, A Hybrid System Approach, Proceedings of the 36th IEEE Conference on Decision and Control, (1997), 4720–4725.
  • [3] B. E. Bishop, M. W. Spong, Control of Redundant Manipulators Using Logic-Based Switching, Proceedings of the 36th IEEE Conference on Decision and Control, (1998), 16–18.
  • [4] W. Zhang, M. S. Branicky, S. M. Phillips, Stability of Networked Control Systems, IEEE Control Systems Magazine, 21(1) (1998), 84–99.
  • [5] D. Z. Chen, Y. J. Guo, Advances on Switched Systems, Control Theory and Applications, 22(6) (2005), 954–960.
  • [6] H. Lin and P. J. Antsaklis, Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, IEEE Trans. Automat. Contr., 54(2) (2009), 308-322.
  • [7] J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, Proc. of the 38th Conf. on Decision and Control, (1999), 2655–2660.
  • [8] O¨ . Karabacak, Dwell time and average dwell time methods based on the cycle ratio of the switching graph, Systems Control Lett., 62(2013), 1032–1037.
  • [9] A. Ya. Bulgakov, An effectively calculable parameter for the stability quality of systems of linear differential equations with constant coefficients, Siberian Math. J., 21(1980), 339–347.
  • [10] A. Ya. Bulgakov, Matrix Computations with Guaranteed Accuracy in Stability Theory, Selc¸uk University, The Research Center of Applied Mathematics, Konya, 1995.
  • [11] S. K. Godunov, Ordinary Differential Equations with Constant Coefficients, Translations of Mathematical Monographs, 169, American Mathematical Society, Providence, RI, 1997.
  • [12] H. Bulgak, Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability, in Error Control and Adaptivity in Scientific Computing, eds. H. Bulgak and C. Zenger, NATO Science Series, Series C: Mathematical and Physical Sciences, 536 (Kluwer Academic Publishers, Dordrecht, 1999), 95–124.
  • [13] A. Duman, K. Aydın, Sensitivity of Hurwitz stability of linear differential equation systems with constant coefficients, Int. J. Geom. Methods Mod. Phys., 14 (2017), 1750084.
  • [14] S. K. Godunov, Modern Aspects of Linear Algebra, Translations of Mathematical Monographs, 175, American Mathematical Society, Providence, RI, 1998.
  • [15] Y. M. Nechepurenko, Bounds for the matrix exponential based on the Lyapunov equation and limits of yhe ,Hausdorff set, Computational Mathematics and Mathematical Physics, 42(2) (2002), 125-134.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ahmet Duman

Yayımlanma Tarihi 15 Mart 2022
Gönderilme Tarihi 8 Ocak 2022
Kabul Tarihi 21 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 1

Kaynak Göster

APA Duman, A. (2022). Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Universal Journal of Mathematics and Applications, 5(1), 10-14. https://doi.org/10.32323/ujma.1055172
AMA Duman A. Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Univ. J. Math. Appl. Mart 2022;5(1):10-14. doi:10.32323/ujma.1055172
Chicago Duman, Ahmet. “Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems”. Universal Journal of Mathematics and Applications 5, sy. 1 (Mart 2022): 10-14. https://doi.org/10.32323/ujma.1055172.
EndNote Duman A (01 Mart 2022) Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Universal Journal of Mathematics and Applications 5 1 10–14.
IEEE A. Duman, “Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems”, Univ. J. Math. Appl., c. 5, sy. 1, ss. 10–14, 2022, doi: 10.32323/ujma.1055172.
ISNAD Duman, Ahmet. “Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems”. Universal Journal of Mathematics and Applications 5/1 (Mart 2022), 10-14. https://doi.org/10.32323/ujma.1055172.
JAMA Duman A. Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Univ. J. Math. Appl. 2022;5:10–14.
MLA Duman, Ahmet. “Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems”. Universal Journal of Mathematics and Applications, c. 5, sy. 1, 2022, ss. 10-14, doi:10.32323/ujma.1055172.
Vancouver Duman A. Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Univ. J. Math. Appl. 2022;5(1):10-4.

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