Finite Time Interval Observer Design for Discrete-Time Switched Systems

  • Jun HuangEmail author
  • Shanen Yu
  • Xiang Ma
  • Liang Chen
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


This paper studies the finite time interval observer design method for discrete-time switched systems. Firstly, some necessary preliminary as well as the framework of finite time interval observer is presented. Then, the sufficient conditions are derived by the forms of linear programming, under which the error system is both positive and finite time bounded. Finally, a numerical example is provided to show the effectiveness of the proposed method.


Finite time Interval observer Linear programming 



This work is supported by National Natural Science Foundation of China (61403267), Natural Science Foundation of Jiangsu Province (BK20130322), and China Postdoctoral Science Foundation (2017M611903).


  1. 1.
    Agresti, A., Coull, B.A.: Approximate is better than exact for interval estimation of binomial proportions. Am. Stat. 52(2), 119–126 (1998)MathSciNetGoogle Scholar
  2. 2.
    Arcak, M., Kokotovi, P.: Nonlinear observers: a circle criterion design and robustness analysis. Automatica 37(12), 1923–1930 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control. 43(4), 475–482 (1998)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bolajraf, M., Ait Rami, M.: A robust estimation approach for uncertain systems with perturbed measurements. Int. J. Robust Nonlinear Control. 26(4), 834–852 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    DeCarlo, R.A., Branicky, M.S., Pettersson, S., et al.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88(7), 1069–1082 (2000)CrossRefGoogle Scholar
  6. 6.
    Degue, K.H., Efimov, D., Le Ny, J.: Interval observer approach to output stabilization of linear impulsive systems. IFAC-PapersOnLine 50(1), 5085–5090 (2017)CrossRefGoogle Scholar
  7. 7.
    Du H., Lin X., Li S.: Finite-time stability and stabilization of switched linear systems. In: IEEE Conference on Decision and Control, pp. 1938–1943 (2010)Google Scholar
  8. 8.
    Efimov, D., Rassi, T., Chebotarev, S., et al.: Interval state observer for nonlinear time varying systems. Automatica 49(1), 200–205 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ethabet, H., Raissi, T., Amairi, M., et al.: Interval observers design for continuous-time linear switched systems. IFAC-PapersOnLine 50(1), 6259–6264 (2017)CrossRefGoogle Scholar
  10. 10.
    Farina, L., Rinaldi, S.: Positive Linear Systems: Theory and Applications. Wiley, New York (2000)CrossRefGoogle Scholar
  11. 11.
    Gouz, J.L., Rapaport, A., Hadj-Sadok, M.Z.: Interval observers for uncertain biological systems. Ecol. Model. 133(1–2), 45–56 (2000)CrossRefGoogle Scholar
  12. 12.
    Guo, S., Zhu, F.: Interval observer design for discrete-time switched system. IFAC-PapersOnLine 50(1), 5073–5078 (2017)CrossRefGoogle Scholar
  13. 13.
    Hu, B., Zhai, G., Michel, A.N.: Common quadratic Lyapunov-like functions with associated switching regions for two unstable second-order LTI systems. Int. J. Control. 75(14), 1127–1135 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hamdi, F., Manamanni, N., Messai, N., et al.: Hybrid observer design for linear switched system via differential Petri nets. Nonlinear Anal. Hybrid Syst. 3(3), 310–322 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    He, Z., Xie, W.: Control of non-linear switched systems with average dwell time: interval observer-based framework. IET Control. Theory Appl. 10(1), 10–16 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ibrir, S.: Circle-criterion approach to discrete-time nonlinear observer design. Automatica 43(8), 1432–1441 (2007)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kharkovskaya T., Efimov D., Polyakov A., et al.: Interval observers for PDEs: approximation approach. In: Proceedings of 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS) (2017)Google Scholar
  18. 18.
    Mazenc, F., Bernard, O.: Interval observers for linear time-invariant systems with disturbances. Automatica 47(1), 140–147 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Rami M.A., Cheng C.H., De Prada.C.: Tight robust interval observers: an LP approach. In: Proceedings of 47th IEEE CDC 2008, pp. 2967–2972 (2008)Google Scholar
  20. 20.
    Serres, U., Vivalda, J.C., Riedinger, P.: On the convergence of linear switched systems. IEEE Trans. Autom. Control. 56(2), 320–332 (2011)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Tanwani, A., Shim, H., Liberzon, D.: Observability for switched linear systems: characterization and observer design. IEEE Trans. Autom. Control. 58(4), 891–904 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Wang, Y., Bevly, D.M., Rajamani, R.: Interval observer design for LPV systems with parametric uncertainty. Automatica 60(10), 79–85 (2015)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhao, X., Zhang, L., Shi, P., et al.: Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control. 57(7), 1809–1815 (2012)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhao, X., Liu, H., Zhang, J., et al.: Multiple-mode observer design for a class of switched linear systems. IEEE Trans. Autom. Sci. Eng. 12(1), 272–280 (2015)CrossRefGoogle Scholar
  25. 25.
    Zheng, G., Efimov, D., Bejarano, F.J., et al.: Interval observer for a class of uncertain nonlinear singular systems. Automatica 71, 159–168 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringSoochow UniversitySuzhouChina
  2. 2.School of AutomationHangzhou Dianzi UniversityHangzhouPeople’s Republic of China

Personalised recommendations