Skip to main content
SpringerLink
Log in

Finite Time Interval Observer Design for Discrete-Time Switched Systems

  • Chapter
  • First Online:
Positive Systems (POSTA 2018)

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 480))

Included in the following conference series:

  • 484 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agresti, A., Coull, B.A.: Approximate is better than exact for interval estimation of binomial proportions. Am. Stat. 52(2), 119–126 (1998)

    MathSciNet  Google Scholar 

  2. Arcak, M., Kokotovi, P.: Nonlinear observers: a circle criterion design and robustness analysis. Automatica 37(12), 1923–1930 (2001)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Efimov, D., Rassi, T., Chebotarev, S., et al.: Interval state observer for nonlinear time varying systems. Automatica 49(1), 200–205 (2013)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  10. Farina, L., Rinaldi, S.: Positive Linear Systems: Theory and Applications. Wiley, New York (2000)

    Book  Google Scholar 

  11. Gouz, J.L., Rapaport, A., Hadj-Sadok, M.Z.: Interval observers for uncertain biological systems. Ecol. Model. 133(1–2), 45–56 (2000)

    Article  Google Scholar 

  12. Guo, S., Zhu, F.: Interval observer design for discrete-time switched system. IFAC-PapersOnLine 50(1), 5073–5078 (2017)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  16. Ibrir, S.: Circle-criterion approach to discrete-time nonlinear observer design. Automatica 43(8), 1432–1441 (2007)

    Article  MathSciNet  Google Scholar 

  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. Mazenc, F., Bernard, O.: Interval observers for linear time-invariant systems with disturbances. Automatica 47(1), 140–147 (2011)

    Article  MathSciNet  Google Scholar 

  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. Serres, U., Vivalda, J.C., Riedinger, P.: On the convergence of linear switched systems. IEEE Trans. Autom. Control. 56(2), 320–332 (2011)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  22. Wang, Y., Bevly, D.M., Rajamani, R.: Interval observer design for LPV systems with parametric uncertainty. Automatica 60(10), 79–85 (2015)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou, China

    Jun Huang, Xiang Ma & Liang Chen

  2. School of Automation, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Shanen Yu

Authors
  1. Jun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shanen Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiang Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Huang .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Hong Kong, Hong Kong, Hong Kong

    James Lam

  2. Hangzhou Dianzi University, Hangzhou, China

    Yun Chen

  3. Southwest Minzu University, Chengdu, China

    Xingwen Liu

  4. Dalian University of Technology, Dalian, China

    Xudong Zhao

  5. Hangzhou Dianzi University, Hangzhou, China

    Junfeng Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Huang, J., Yu, S., Ma, X., Chen, L. (2019). Finite Time Interval Observer Design for Discrete-Time Switched Systems. In: Lam, J., Chen, Y., Liu, X., Zhao, X., Zhang, J. (eds) Positive Systems . POSTA 2018. Lecture Notes in Control and Information Sciences, vol 480. Springer, Cham. https://doi.org/10.1007/978-3-030-04327-8_7

Download citation

Publish with us

Policies and ethics

Search

Navigation