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Observers for controllers with matched uncertainty in A, B and C matrices

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 170))

Abstract

In this paper, the effects of using observers on robust linear state feedback controllers are studied. The uncertainty, which can enter A, B or C matrices, is assumed to satisfy certain matching conditions. Lyapunov techniques are used to establish sufficient condition for stability for a given uncertainty bound. In particular, sufficient conditions are obtained that, if met, guarantee stabilization regardless of the size of the uncertainty.

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References

  1. A.R Galimidi and B.R. Barmish, “The constrained Lyapunov problem and its application to robust output stabilization,” IEEE Transactions on Automatic Control, vol. 31, pp. 410–419, 1986.

    Google Scholar 

  2. B.R. Barmish and A.R. Galimidi, “Robustness of Luenberger observers: linear systems stabilized via nonlinear control,” Automatica, vol. 22, pp. 413–423, 1986.

    Google Scholar 

  3. V.W. Breinl and P.C. Muller, “Ein parameterunempfindlicher zustandsbobacher und seine anwendung bei einem tragregelsystem eines magnetschwebefahrzeugs,” Regelungstechnik, vol. 30, pp. 403–412, 1982.

    Google Scholar 

  4. V.W. Breinl and G. Leitmann, “State feedback for uncertain dynamical systems,” Applied Mathematics and Computation, vol. 22, pp. 65–87, 1987.

    Google Scholar 

  5. I.R. Petersen, “A Riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems,” IEEE Transactions on Automatic Control, vol. 30, pp. 904–907, September 1985.

    Google Scholar 

  6. I.R. Petersen and C.V. Hollot, “High gain observers applied to problems in stabilization of uncertain linear systems, disturbance attenuation and H optimization,” International of Adaptive Control and Signal Processing, vol. 2, pp. 347–369, 1988.

    Google Scholar 

  7. F. Jabbari and W.E. Schmitendorf, “Robust linear controllers using observers,” 1990. To appear in IEEE Trans. on Automatic Control.

    Google Scholar 

  8. F. Jabbari and W.E. Schmitendorf, “Effects of observers on stabilization of linear uncertain system,” Proceedings of 1991 ACC.

    Google Scholar 

  9. M. Tahk and J.L. Speyer, “Modeling of parameter variations and asymptotic LQG synthesis,” IEEE Transactions on Automatic Control, vol. 32, pp. 793–801, September 1987.

    Google Scholar 

  10. F. Jabbari and W.E. Schmitendorf, “A non-iterative method for design of linear robust controllers,” IEEE Transactions on Automatic Control, vol. 35, pp. 2954–957, August 1990.

    Google Scholar 

  11. H. Kano, “Existence condition of positive definite solutions for algebraic matrix Riccati equations,” Automatica, vol. 23, pp. 393–397, June 1987.

    Google Scholar 

  12. B.A. Francis, “The optimal linear quadratic time invariant regulator with cheap control,” IEEE Transactions on Automatic Control, vol. 24, pp. 616–621, August 1979.

    Google Scholar 

  13. T. Kailath, Linear Systems. New Jersey: Prentice-Hall, 1980.

    Google Scholar 

  14. R.J. Veillette, J.V. Medanic, and W.R. Perkins, “Robust stabilization and disturbance rejection for systems with structured uncertainty,” In 28th IEEE Conference on Decision and Control, (Tampa, Florida), pp. 936–941, December 1989.

    Google Scholar 

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Authors

Editor information

Janislaw M. Skowronski Henryk Flashner Ramesh S. Guttalu

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© 1992 Springer-Verlag

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Jabbari, F. (1992). Observers for controllers with matched uncertainty in A, B and C matrices. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004309

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  • DOI: https://doi.org/10.1007/BFb0004309

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54954-3

  • Online ISBN: 978-3-540-46606-2

  • eBook Packages: Springer Book Archive

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