Skip to main content

Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 75))

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. Banks, H.T. and Burns, J.A.: Hereditary control problems: Numerical methods based on averaging approximation, SIAM J. Control Optimization 16 (1978), pp. 169–208

    Google Scholar 

  2. Banks, H.T. and Kappel, F.: Spline approximations for functional differential equations, J. Differential Eq. 34 (1979), pp. 496–522.

    Google Scholar 

  3. Curtain, R.F. and Pritchard, A.J.: The infinite dimensional Riccati equation for systems defined by evolution operators, SIAM J. Control Optimization 14 (1976), pp. 951–983.

    Google Scholar 

  4. Ehle, B.L.: A-stable methods and Padé approximations to the exponential, SIAM J. Math. Anal. 4 (1973), pp. 671–680.

    Google Scholar 

  5. Gibson, J.S.: Linear-quadratic optimal control of hereditary differential systems: Infinite dimensional Riccati equations and numerical approximations, SIAM J. Control Optimization 21 (1983), pp. 95–139.

    Google Scholar 

  6. Ito, K. and Teglas, R.: Legendre-tau approximation for functional differential equations, ICASE Report 83-17, NASA Langley Research Center, Hampton, VA, June 1983.

    Google Scholar 

  7. Ito, K. and Teglas, R.: Leendre-tau approximation for functional differential equations, Part II: The linear quadratic optimal control problem, ICASE Report 84-31, NASA Langley Research Center, Hampton, VA. July 1984.

    Google Scholar 

  8. Manitius, A.: Optimal control of hereditary systems, Lecture Notes in Control Theory and Topics in Functional Analysis, Vol. III, pp. 43–128, International Atomic Energy Agency, Vienna (1976).

    Google Scholar 

  9. Salamon, D.: Structure and stability of finite dimensional approximations for functional differential equations, MRC Report #2586, University of Wisconsin, Madison, WI, October 1983.

    Google Scholar 

  10. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.

    Google Scholar 

  11. Vinter, R.B.: Filter stability for stochastic evaluation equations, SIAM J. Control Optimization 15 (1977), pp. 465–485.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Franz Kappel Karl Kunisch Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Ito, K. (1985). Legendre-tau approximation for functional differential equations part III: Eigenvalue approximations and uniform stability. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005653

Download citation

  • DOI: https://doi.org/10.1007/BFb0005653

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15872-1

  • Online ISBN: 978-3-540-39661-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics