Design of Luenberger Observers for a Class of Hybrid Linear Systems

  • A. Alessandri
  • P. Coletta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2034)

Abstract

An approach to estimation for a class of hybrid discrete-time linear systems using Luenberger observers is presented. The proposed Luenberger observer for such a kind of systems relies on the switching among different gains. Convergence conditions have been found to ensure the stability of the error dynamics and the related gains may be selected by solving a set of linear matrix inequalities (LMIs). Moreover, this observer may be improved by suitably updating the estimate using the last measures. This update enables one to reduce the norm of the estimation error and is based on the so-called projection method. Simulation results are reported to show the effectiveness of these methods in the estimation for hybrid discrete-time linear systems.

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References

  1. 1.
    Ackerson, G. A., Fu, K. S.: On state estimation in switching environments. IEEE Trans. on Automatic Control. 15 (1970) 10–17CrossRefGoogle Scholar
  2. 2.
    Zhang, Q.: Hybrid filtering for linear systems with non-Gaussian disturbances. IEEE Trans. on Automatic Control. 45 (1999) 50–61CrossRefGoogle Scholar
  3. 3.
    Doucet, A., Logothetis, A., and Krishnamurthy, V.: Stochastic sampling algorithms for state estimation of jump markov linear systems. IEEE Trans. on Automatic Control. 45 (2000) 188–202MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bar-Shalom, Y., Li, X.: Estimation and Tracking. Artech House, Boston-London (1993)MATHGoogle Scholar
  5. 5.
    Liu, Y.: Switching observer design for uncertain nonlinear systems. IEEE Trans. on Automatic Control. 42 (1997) 1699–1703MATHCrossRefGoogle Scholar
  6. 6.
    Yao, Y. X., Darouach, M., and Schaefers J.: Simultaneous observation of linear systems. IEEE Trans. on Automatic Control. 40 (1995) 696–699MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ye, H., Michel, A. N., and Hou, L.: Stability theory for hybrid dynamical systems. IEEE Trans. on Automatic Control, 43 (1998) 461–474MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Branicky, M. S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. on Automatic Control. 43 (1998) 475–482MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Liberzon, D., Morse, A. S.: Basic problems in stability and design of switched systems. IEEE Control Systems Magazine. 19 (1999) 59–70CrossRefGoogle Scholar
  10. 10.
    Sur, J.: State Observers for Linear Systems with Quantized Outputs. PhD thesis, University of California, Santa Barbara (1996)Google Scholar
  11. 11.
    Sur, J., Healey, A. J.: A multi sensor asynchronous projection algorithm filter (PAF) for AUV navigation. in 10th Symposium on Unmanned Untethered Submersible Technology, Durham, New Hampshire, (1997) 88–100Google Scholar
  12. 12.
    Boyd, S., Crusius, C., and Hanson, A.: Control applications of nonlinear convex programming. J. Proc. Control. 8 (1998) 313–324CrossRefGoogle Scholar
  13. 13.
    Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics. 15 (1994) SIAM, Philadelphia, PAGoogle Scholar
  14. 14.
    Alessandri, A., Coletta, P.: Navigation for underwater vehicles based on nonlinear asynchronous estimation. Proc. American Control Conference, Chicago, IL (2000) 85–89Google Scholar
  15. 15.
    Gahinet, P., Nemirovski, A., and Laub, A. J., and Chilali, M.: LMI Control Toolbox User’s Guide. The Math Works Inc. (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • A. Alessandri
    • 1
  • P. Coletta
    • 1
    • 2
  1. 1.IAN-CNR National Research Council of ItalyNaval Automation InstituteGenovaItaly
  2. 2.Department of Communications, Computer and System SciencesDIST-University of GenoaGenovaItaly

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