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A Model Matching Solution of Robust Observer Design for Time-Delay Systems

  • Anas Fattouh
  • Olivier Sename
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 38)

Abstract

Uncertainties arc unavoidable in practical situations and they have to be taken into consideration in control system design. In this chapter, a method for designing a robust observer for linear time-delay systems is proposed. Under the assumption that the considered time-delay system is spectrally controllable and spectrally observable, a double Bézout factorization of its nominal transfer matrix is obtained. Next, based on this factorization, all stable observers for the nominal system are parameterized. By applying those observers on the real system, the parameterization transfer matrix has to be found such that the error between the real estimation and the nominal one is minimized. This problem is rewritten as an infinite dimensional model matching problem for different types of uncertainty. In order to solve this infinite dimensional model matching problem, it is transformed into a finite dimensional one, and therefore a suboptimal solution can be obtained using existing algorithms.

Keywords

Transfer Matrix Real Estimation Suboptimal Solution Stable Polynomial Unknown Input Observer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Doyle, J. C., B. A. Francis and A. R. Tannenbaum (1992). Feedback control theory. Macmillan Publishing Company.Google Scholar
  2. 2.
    Dugard, L. and E.I. Verriest (1998). Stability and control of time-delay systems. Springer.Google Scholar
  3. 3.
    Fattouh, A., O. Sename and J.-M. Dion (1998). H∞ observer design for time-delay systems. In ‘Proc. 37th IEEE Confer. on Decision & Control’. Tampa, Florida, USA. pp. 4545–4546.Google Scholar
  4. 4.
    Fattouh, A., O. Sename and J.-M. Dion (l999a). ‘Robust observer design for time-delay systems: A Riccati equation approach’. Kybemetika 35(6), 753–764.MathSciNetGoogle Scholar
  5. 5.
    Fattouh, A., O. Sename and J.-M. Dion (l999b). An unknown input observer design for linear time-delay systems. In ‘Proc. 38th IEEE Confer. on Decision & Control’. Phoenix, Arizona, USA. pp. 4222–4227.Google Scholar
  6. 6.
    Fattouh, A., O. Sename and J.-M. Dion (2000). Robust observer design for linear uncertain time-delay systems: A factorization approach. In ‘14th Int. Symp. on Mathematical Theory of Networks and Systems’. Perpignan, France, June, 19–23.Google Scholar
  7. 7.
    Fiagbedzi, Y. A. and A. E. Pearson (1990). ‘Exponential state observer for time-lag systems’. Int. Journal of Cotrol 51(1), 189–204.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Francis, B. (1987). A course in H∞ control theory. Springer-Verlag.Google Scholar
  9. 9.
    Kamen, E. W., P. P. Khargonekar and A. Tannenbaum (1986). ‘Proper stable beZOut factorizations and feedback control of linear time-delay systems’, Int. Journal of Control 43(3), 837–857.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Lee, E. B. and A. Olbrot (1981). ‘Observability and related structural results for linear hereditary system’. Int. Journal of Control 34(6), 1061–1078.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Anas Fattouh
    • 1
  • Olivier Sename
    • 2
  1. 1.Automatic Laboratory of Aleppo, Faculty of Electrical and Electronic EngineeringUniversity of AleppoAleppoSyria
  2. 2.LAG, ENSIEG-BP 46Saint Manin d’Hères CedexFrance

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