Advertisement

Stability of Discrete-time Switched Positive Linear Systems with Mode-dependent Average Dwell Time

  • Li-Juan Liu
  • Xudong ZhaoEmail author
  • Xi-Ming Sun
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)

Abstract

This paper concerns the problem of stability for the discrete-time switched positive linear systems with mode-dependent average dwell time. By proposing a novel multiple discontinuous co-positive Lyapunov function approach, the conditions of stability are established for such system based on linear programming. Compared with the existing work, it turns out that our proposed approach produces less conservative results because of providing smaller bounds on the dwell time. A numerical example is given to show the effectiveness of our approach.

Keywords

Switched systems Positive systems Stability Multiple discontinuous co-positive Lyapunov function Mode-dependent average dwell time 

References

  1. 1.
    De Leenheer, P., Aeyels, D.: Stabilization of positive linear systems. Syst. Control Lett. 44(4), 259–271 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Farina, L., Rinaldi, S.: Positive Linear Systems: Theory and Applications. Wiley, New Jercy (2011)zbMATHGoogle Scholar
  3. 3.
    Gurvits, L., Shorten, R., Mason, O.: On the stability of switched positive linear systems. IEEE Trans. Autom. Control 52(6), 1099–1103 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kaczorek, T.: Positive 1D and 2D Systems. Springer Science & Business Media, Berlin (2012)zbMATHGoogle Scholar
  5. 5.
    Knorn, F., Mason, O., Shorten, R.: On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica 45(8), 1943–1947 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lian, J., Liu, J.: New results on stability of switched positive systems: an average dwell-time approach. IET Control Theory Appl. 7(12), 1651–1658 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Liberzon, D.: Switching in Systems and Control. Springer Science & Business Media, Berlin (2012)zbMATHGoogle Scholar
  8. 8.
    Lin, H., Antsaklis, P.J.: Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308–322 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Liu, X.: Stability analysis of switched positive systems: a switched linear co-positive Lyapunov function method. IEEE Trans. Circuits Syst. II Expr. Briefs 56(5), 414–418 (2009)CrossRefGoogle Scholar
  10. 10.
    Liu, X., Yu, W., Wang, L.: Stability analysis for continuous-time positive systems with time-varying delays. IEEE Trans. Autom. Control 55(4), 1024–1028 (2010)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Liu, L.J., Zhao, X., Sun, X.M., Zong, G.D.: Stability and \(l_2\)-gain analysis of discrete-time switched systems with mode-dependent average dwell time. IEEE Trans. Syst. Man Cybern. Syst. https://doi.org/10.1109/TSMC.2018.2794738 (2018)
  12. 12.
    Rami, M.A., Tadeo, F.: Controller synthesis for positive linear systems with bounded controls. IEEE Trans. Circuits Syst. II Expr. Briefs 54(2), 151–155 (2007)CrossRefGoogle Scholar
  13. 13.
    Shu, Z., Lam, J., Gao, H., et al.: Positive observers and dynamic output-feedback controllers for interval positive linear systems. IEEE Trans. Circuits Syst. I Regul. Pap. 55(10), 3209–3222 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sun, X.M., Zhao, J., Hill, D.J.: Stability and \(L_2\)-gain analysis for switched delay systems: a delay-dependent method. Automatica 42(10), 1769–1774 (2006)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, L., Shi, P.: Stability, \(l_2\)-Gain and asynchronous \(H_\infty \) control of discrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2192–2199 (2009)CrossRefGoogle Scholar
  16. 16.
    Zhang, J., Han, Z., Zhu, F., Huang, J.: Stability and stabilization of positive switched systems with mode-dependent average dwell time. Nonlinear Anal. Hybrid Syst. 9, 42–55 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhao, X., Yin, Y., Liu, L., Sun, X.: Stability analysis and delay control for switched positive linear systems. IEEE Trans. Autom. Control 63(7), 2184–2190 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhao, X., Zhang, L., Shi, P.: Stability of a class of switched positive linear time-delay systems. Int. J. Robust Nonlinear Control 23(5), 578–589 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhao, X., Zhang, L., Shi, P., Liu, M.: Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zhao, X., Zhang, L., Shi, P., Liu, M.: Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Control Science and EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.School of SoftwareDalian Jiaotong UniversityDalianPeople’s Republic of China

Personalised recommendations