Skip to main content
SpringerLink
Log in

New ℋ2 Filter for Uncertain Singular Systems Using Strict LMIs

  • Published:
Circuits, Systems & Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, the robust ℋ2 filtering problem for a class of linear singular systems with norm-bounded uncertainties is investigated. A class of linear regular filters, which can be realized in practice, is fully analyzed, and then necessary and sufficient conditions for ℋ2 performance of the filtered system are provided. It is established that the solution to the filtering design problem can be cast in the format of strict linear matrix inequalities (LMIs). A numerical example is worked out to illustrate the theoretical developments.

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. B.D.O. Anderson, J.B. Moore, Optimal Filtering (Prentice-Hall, New York, 1979)

    MATH  Google Scholar 

  2. D.S. Bernstein, W.M. Haddad, Steady-state Kalman filtering with an ℋ∞ error bound. Syst. Control Lett. 16, 309–317 (1991)

    Article  MathSciNet  Google Scholar 

  3. S. Boyd, L. ElGhaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

    MATH  Google Scholar 

  4. S.J. Chen, J.L. Lin, Robust stability of discrete time-delay uncertain singular systems. IEE Proc. Control Theory Appl. 151, 45–51 (2004)

    Article  MathSciNet  Google Scholar 

  5. L. Dai, Singular Control Systems (Springer, Berlin, 1989)

    Book  MATH  Google Scholar 

  6. Z. Duan, J. Zhang, C. Zhang, E. Mosca, Robust ℋ2 and ℋ∞ filtering for uncertain linear systems. Automatica 42, 1919–1926 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. L. ElGhaoui, F. Oustry, M. Ait Rami, A cone complementarity linearization algorithm for static output feedback control and related problems. IEEE Trans. Automat. Control. 42, 1171–1176 (1997)

    Article  MathSciNet  Google Scholar 

  8. M. Fu, C.E. de Souza, L. Xie, ℋ∞-estimation for uncertain systems. Int. J. Robust Nonlinear Control 2, 87–105 (1992)

    Article  MATH  Google Scholar 

  9. P. Gahinet, P. Apkarian, A linear matrix inequality approach to ℋ∞ control. Int. J. Robust Nonlinear Control 4, 421–448 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Gao, J. Lam, L.H. Xie, C. Wang, New approach to mixed ℋ2ℋ2 /ℋ∞ filtering for polytopic discrete-time systems. IEEE Trans. Signal Process. 53, 3183–3192 (2005)

    Article  MathSciNet  Google Scholar 

  11. H. Gao, X. Meng, T. Chen, A new design of robust ℋ2 filters for uncertain systems. Syst. Control Lett. 57, 585–593 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. J.C. Geromel, Optimal linear filtering with parameter uncertainty. IEEE Trans. Signal Process. 47, 168–175 (1999)

    Article  MATH  Google Scholar 

  13. D.W.C. Ho, G. Lu, Robust stabilization of a class of discrete-time nonlinear systems via output feedback: the unified LMI approach. Int. J. Control 76, 105–115 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. H.K. Khalil, Nonlinear systems, 3rd edn. (Prentice-Hall, New York, 2002)

    MATH  Google Scholar 

  15. F.L. Lewis, A survey of linear singular systems. Circuits Syst. Signal Process. 5, 3–36 (1986)

    Article  MATH  Google Scholar 

  16. C. Lin, J.L. Wang, C.B. Soh, Robustness of uncertain descriptor systems. Syst. Control Lett. 31, 129–138 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. G. Lu, D.W.C. Ho, Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation. IEEE Trans. Automat. Control 51, 818–823 (2006)

    Article  MathSciNet  Google Scholar 

  18. M.S. Mahmoud, Resilient linear filtering of uncertain systems. Automatica 40, 1797–1802 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. M.S. Mahmoud, Resilient Control of Uncertain Dynamical Systems (Springer, Berlin, 2004)

    MATH  Google Scholar 

  20. M.S. Mahmoud, Resilient ℒ2/ℒ∞ filtering of polytopic systems with state-delays. Proc. IET Control Theory Appl. 1, 141–151 (2007)

    Article  MathSciNet  Google Scholar 

  21. M.S. Mahmoud, A.A. Boujarwah, Robust ℋ∞ filtering for a class of linear parameter-varying systems. IEEE Trans. Circuits Syst. I 48, 1131–1138 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  22. M.S. Mahmoud, P. Shi, Robust Kalman filtering for continuous time-lag systems with jump parameters. IEEE Trans. Circuits Syst. I 50, 98–105 (2003)

    Article  MathSciNet  Google Scholar 

  23. M.S. Mahmoud, N.F. Al-Muthairi, S. Bingulac, Robust Kalman filtering for continuous time-lag systems. Syst. Control Lett. 38, 309–319 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. K.M. Nagpal, P.P. Khargonekar, Filtering and smoothing in ℋ∞ setting. IEEE Trans. Automat. Control 36, 152–166 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  25. A. Rehm, F. Allgower, Self-scheduled ℋ∞ output feedback control of descriptor systems. Comput. Chem. Eng. 24, 279–284 (2000)

    Article  Google Scholar 

  26. M. Sato, Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions. Automatica 42, 2017–2023 (2006)

    Article  MATH  Google Scholar 

  27. K. Takaba, T. Katayama, Robust ℋ2 performance of uncertain descriptor systems, in Proc. 1997 European Control Conference, WE-E-B-2 (1997)

  28. E. Uezato, M. Ikeda, Strict LMI conditions for stability, robust stabilization and ℋ∞ control of descriptor systems, in Proc. the 38th Conf. Decision and Control, Arizona, December 1999, pp. 4092–4097

  29. L.H. Xie, L. Lu, H. Zhang, Improved robust ℋ2 and ℋ∞ filtering for uncertain discrete-time systems. Automatica 40, 873–880 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. S. Xu, J. Lam, Robust stability and stabilization of discrete singular systems: an equivalent characterization. IEEE Trans. Automat. Control 49, 568–574 (2004)

    Article  MathSciNet  Google Scholar 

  31. S. Xu, P.V. Dooren, R. Stefan, J. Lam, Robust stability and stabilization for singular systems with state-delay and parameter uncertainty. IEEE Trans. Automat. Control 47, 1122–1228 (2002)

    Article  MathSciNet  Google Scholar 

  32. S. Xu, J. Lam, Y. Zou, ℋ∞ filtering for singular systems. IEEE Trans. Automat. Control 48, 2217–2222 (2003)

    Article  MathSciNet  Google Scholar 

  33. D. Yue, Q.L. Han, Robust ℋ∞ filter design of uncertain descriptor systems with discrete and distributed delays. IEEE Trans. Signal Process. 52, 3200–3212 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 1783, Dhahran, 31261, Saudi Arabia

    Magdi S. Mahmoud & Hosam E. Emara-Shabaik

Authors
  1. Magdi S. Mahmoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hosam E. Emara-Shabaik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Magdi S. Mahmoud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahmoud, M.S., Emara-Shabaik, H.E. New ℋ2 Filter for Uncertain Singular Systems Using Strict LMIs. Circuits Syst Signal Process 28, 665–677 (2009). https://doi.org/10.1007/s00034-009-9102-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-009-9102-y

Keywords

Search

Navigation