Research Article

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

Volume: 5 Number: 1 March 15, 2022
EN

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

Abstract

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.

Keywords

Differential equation systems, Hurwitz stability, Switched system, Dwell time

References

  1. [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. [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. [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. [4] W. Zhang, M. S. Branicky, S. M. Phillips, Stability of Networked Control Systems, IEEE Control Systems Magazine, 21(1) (1998), 84–99.
  5. [5] D. Z. Chen, Y. J. Guo, Advances on Switched Systems, Control Theory and Applications, 22(6) (2005), 954–960.
  6. [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. [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. [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. [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. [10] A. Ya. Bulgakov, Matrix Computations with Guaranteed Accuracy in Stability Theory, Selc¸uk University, The Research Center of Applied Mathematics, Konya, 1995.
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
1.Duman A. Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Univ. J. Math. Appl. 2022;5(1):10-14. doi:10.32323/ujma.1055172
Chicago
Duman, Ahmet. 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.
EndNote
Duman A (March 1, 2022) Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Universal Journal of Mathematics and Applications 5 1 10–14.
IEEE
[1]A. Duman, “Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems”, Univ. J. Math. Appl., vol. 5, no. 1, pp. 10–14, Mar. 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 (March 1, 2022): 10-14. https://doi.org/10.32323/ujma.1055172.
JAMA
1.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, vol. 5, no. 1, Mar. 2022, pp. 10-14, doi:10.32323/ujma.1055172.
Vancouver
1.Ahmet Duman. Dwell Time for the Hurwitz Stability of Switched Linear Differential Equation Systems. Univ. J. Math. Appl. 2022 Mar. 1;5(1):10-4. doi:10.32323/ujma.1055172