Skip to main content

Spectral theory of linear control and estimation problems

  • Identification, Estimation, Filtering
  • Conference paper
  • First Online:
  • 93 Accesses

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 14))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. C. Willems, "Least squares stationary optimal control and the algebraic Riccati equation," IEEE Trans. Automat. Contr., Vol. AC-16, pp. 621–634, 1971.

    Article  Google Scholar 

  2. J. M. Rodriguez-Canabal, "The geometry of the Riccati equation," Stochastics, Vol. 1, pp. 129–149, 1973.

    Google Scholar 

  3. R. S. Bucy, "New results in asymptotic control theory," SIAM J. Control, Vol. 4, pp. 397–402, 1966.

    Article  Google Scholar 

  4. L. M. Silverman, "Discrete Riccati equations: alternative algorithms, asymptotic properties, and system theory interpretations," in Control and Dynamic Systems, C. T. Leondes (ed.), Vol. 12, New York: Academic Press, 1976.

    Google Scholar 

  5. J. C. Willems, "On the existence of a nonpositive solution to the Riccati equation," IEEE Trans. Automat. Contr., Vol. AC-19, pp. 592–593, 1974.

    Article  Google Scholar 

  6. B. D. O. Anderson, "Algebraic properties of minimal degree spectral factors," Automatica, Vol. 9, pp. 491–500, 1973.

    Article  Google Scholar 

  7. —, "Corrections to: algebraic properties of minimal degree spectral factors," Automatica, Vol. 11, pp. 321–322, 1975.

    Article  Google Scholar 

  8. J. C. Willems, "Mechanisms for the stability and instability in feedback systems," Proc. IEEE, Vol. 64, pp. 24–35, 1976.

    Google Scholar 

  9. P. Faurre, "Realisations markoviennes de processes stationnaires," IRIA Report, 1972.

    Google Scholar 

  10. M. R. Gevers and T. Kailath, "Constant, predictable, and degenerated directions of the discrete Riccati equation," Automatica, Vol. 9, pp. 699–711, 1973.

    Article  Google Scholar 

  11. —, "An innovation approach to least squares estimation — Part VI: discrete-time innovation representation and recursive estimation," IEEE Trans. Automat. Contr., Vol. AC-18, pp. 588–600, 1973.

    Article  Google Scholar 

  12. G. Picci, "Stochastic realization of Gaussian processes," Proc. IEEE, Vol. 64, pp. 112–122, 1976.

    Google Scholar 

  13. E. A. Jonckheere and L. M. Silverman, "The general discrete-time linear-quadratic control problem," Proc. IEEE Conf. Decision and Control, New Orleans, Louisiana, pp. 1239–1244, 1977.

    Google Scholar 

  14. —, "Spectral theory of the linear-quadratic optimal control problem: discrete-time single-input case," to appear in IEEE Trans. Circuits and Systems, Special issue on mathematical foundation of system theory, vol. CAS-25, 1978.

    Google Scholar 

  15. —, "Spectral theory of the linear-quadratic optimal control problem: analytic factorization of rational matrix-valued functions," submitted to SIAM J Control and Optimization.

    Google Scholar 

  16. —, "Spectral theory of the linear-quadratic optimal control problem: a new algorithm for spectral computations," submitted to IEEE Trans. Automat. Contr.

    Google Scholar 

  17. E. A. Jonckheere, "Spectral theory of the linear-quadratic optimal control problem," Ph.D. dissertation, University of Southern California, Los Angeles, 1978.

    Google Scholar 

  18. —, "On the observability of the deformable modes in a class of nonrigid satellites," Proc. Symp. Dynamics and Control of Nonrigid Spacecraft, Frascati, Italy, May 24–26, 1976, ESA SP 117, pp. 251–262.

    Google Scholar 

  19. —, "Robustness of observers for estimating the state of a deformable satellite," Conf. on Attitude and Orbit Contr. Systems, Noordwijk, the Netherlands, October 3–6, 1977, Preprints Book, pp. 191–202.

    Google Scholar 

  20. F. Riesz and B. Sz.-Nagy, Leçons d' Analyse Fonctionnelle. Paris: Gauthier-Villars, 1968.

    Google Scholar 

  21. R. G. Douglas, "Banach algebra techniques in the theory of Toeplitz operators," Regional Conf. Series, Vol. 15, Amer. Math. Soc., Providence, Rhode Island, 1972.

    Google Scholar 

  22. T. Kato, Perturbation Theory for Linear Operators. New York: Springer-Verlag, 1966.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

Jonckheere, E.A., Silverman, L.M. (1979). Spectral theory of linear control and estimation problems. In: Bensoussan, A., Lions, J.L. (eds) International Symposium on Systems Optimization and Analysis. Lecture Notes in Control and Information Sciences, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002645

Download citation

  • DOI: https://doi.org/10.1007/BFb0002645

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09447-0

  • Online ISBN: 978-3-540-35232-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics