Skip to main content
SpringerLink
Log in

Observers for descriptor systems with slope-restricted nonlinearities

  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear matrix inequality (LMI) condition is derived to construct the full-order observer. The existence and uniqueness of the solution to the obtained observer system are guaranteed. Furthermore, under the same LMI condition and a common assumption, a reduced-order observer is designed. Finally, the design methods are reduced to a strict LMI problem and illustrated by a numerical example.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. L. Campbell. Singular Systems of Differential Equations, London, UK: Pitman 1980.

    MATH  Google Scholar 

  2. E. L. Lewis. A survey of linear singular systems. Circuits, Systems and Signal Processing, vol. 5, no. 1, pp. 3–36, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Dai. Singular Control Systems, Berlin, Germany: Springer, 1989.

    Book  MATH  Google Scholar 

  4. X. Z. Dong, Q. L. Zhang. Robust input-output energy decoupling for uncertain singular systems. International Journal of Automation and Computing, vol. 2, no. 1, pp. 37–42, 2005.

    Article  Google Scholar 

  5. B. Zhou, G. R. Duan, Y. L. Wu. Parametric approach for the normal Luenberger function observer design in second-order descriptor linear systems. International Journal of Automation and Computing, vol. 5, no. 2, pp. 125–131, 2008.

    Article  Google Scholar 

  6. M. M. Fahmy, J. O’Reilly. Observers for descriptor systems. International Journal of Control, vol. 49, no. 6, pp. 2013–2028, 1989.

    MATH  MathSciNet  Google Scholar 

  7. M. Darouach, M. Boutayeb. Design of observers for descriptor systems. IEEE Transactions on Automatic Control, vol. 40, no. 7, pp. 1323–1327, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Darouach, M. Zasadzinski, M. Hayar. Reduced-order observer design for descriptor systems with unknown inputs. IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 1068–1072, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Hou, P. C. Muller. Observer design for descriptor systems. IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 164–169, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Koenig, S. Mammar. Design of proportional-integral observer for unknown input descriptor systems. IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 2057–2062, 2002.

    Article  MathSciNet  Google Scholar 

  11. Z. Gao, D. W. C. Ho. State/noise estimator for descriptor systems with application to sensor fault diagnosis. IEEE Transactions on Signal Processing, vol. 54, no. 4, pp. 1316–1326, 2006.

    Article  Google Scholar 

  12. A. G. Wu, G. R. Duan. Design of PD observers in descriptor linear systems. International Journal of Control, Automation, and Systems, vol. 5, no. 1, pp. 93–98, 2007.

    MathSciNet  Google Scholar 

  13. A. G. Wu, G. R. Duan. Design of generalised PI observers in descriptor linear systems. IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 12, pp. 2828–2837, 2006.

    Article  MathSciNet  Google Scholar 

  14. A. G. Wu, G. R. Duan, Y. M. Fu. Generalized PID observer design for descriptor linear systems. IEEE Transactions Systems, Man, and Cybernetics, vol. 37, no. 5, pp. 1390–1395, 2007.

    Article  Google Scholar 

  15. M. Boutayeb, M. Darouach. Observers design for nonlinear descriptor systems. In Proceedings of the 34th IEEE Conference on Decision and Control, IEEE, New Orleans, LA, USA, vol. 3, pp. 2369–2374, 1995.

    Google Scholar 

  16. D. N. Shields. Observer design and detection for nonlinear descriptor systems. International Journal of Control, vol. 67, no. 2, pp. 153–168, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  17. G. Zimmera, J. Meierb. On observing nonlinear descriptor systems. Systems & Control Letters, vol. 32, no. 1, pp. 43–48, 1997.

    Article  MathSciNet  Google Scholar 

  18. J. åslund, E. Frisk. An observer for non-linear differentialalgebraic systems. Automatica, vol. 42, no. 6, pp. 959–965, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  19. D. Koenig. Observer design for unknown input nonlinear descriptor systems via convex optimization. IEEE Transactions on Automatic Control, vol. 51, no. 6, pp. 1047–1052, 2006.

    Article  MathSciNet  Google Scholar 

  20. G. Lu, D. W. C. Ho. Full-order and reduced-order observers for Lipschitz descriptor systems: The unified LMI approach. IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 7, pp. 563–567, 2006.

    Article  Google Scholar 

  21. I. Masubuchi, Y. Kamitane, A. Ohara, N. Suda. H ∞ control for descriptor systems: A matrix inequalities approach. Automatica, vol. 33, no. 4, pp. 669–673, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  22. M. Arcak, P. Kokotovic. Nonlinear observers: A circle criterion design and robustness analysis. Automatica, vol. 37, no. 12, pp. 1923–1930, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Arcak, P. Kokotovic. Observer-based control of systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1146–1150, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  24. X. Fan, M. Arcak. Observer design for systems with multivariable monotone nonlinearities. Systems & Control Letters, vol. 50, no. 4, pp. 319–330, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. Gahinet, A. Nemirovski, A. J. Laub, M. Chilali. LMI Control Toolbox, Technical Report, The Mathworks Inc., 1995.

  26. J. Y. Ishihara, M. H. Terra. On the Lyapunov theorem for singular systems. IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1926–1930, 2002.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Business Administration, Northeastern University, Shenyang, 110004, PRC

    Lin-Na Zhou

  2. Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, 110004, PRC

    Chun-Yu Yang

  3. Institute of Systems Science, Northeastern University, Shenyang, 110004, PRC

    Qing-Ling Zhang

Authors
  1. Lin-Na Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-Yu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qing-Ling Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Yu Yang.

Additional information

This work was supported by National Basic Research Program of China (973 Program) (No. 2009CB320601), National Natural Science Foundation of China (No. 60904009), and Fundamental Research Funds for the Central Universities (No. 100406010, No. 090408001).

Lin-Na Zhou received the B. Sc. degree from the Department of Water Conservancy Engineering of North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou, PRC in 2001 and the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, PRC in 2007. Now, she works at School of Business Administration, Northeastern University, Shenyang, PRC.

Her research interests include descriptor systems, robust control, and fuzzy control.

Chun-Yu Yang received the B. Sc. and the Ph. D. degrees from Northeastern University, Shenyang, PRC in 2002 and 2009, respectively. Now, he works at Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, PRC.

His research interests include descriptor systems, robust control, and fuzzy control.

Qing-Ling Zhang received the B. Sc. and M. Sc. degrees from the Mathematics Department, and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, PRC in 1982, 1986, and 1995, respectively. He finished his two-year post-doctoral work in Department of Automatic Control at Northwestern Polytechnical University, Xi’an, PRC in 1997. Since then, he has been a professor at Northeastern University.

His research interests include descriptor systems, robust control, and networked control systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, LN., Yang, CY. & Zhang, QL. Observers for descriptor systems with slope-restricted nonlinearities. Int. J. Autom. Comput. 7, 472–478 (2010). https://doi.org/10.1007/s11633-010-0529-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-010-0529-1

Keywords

Search

Navigation