Advertisement

Feedback Stabilizibility over Commutative Rings

  • J. W. Brewer
  • L. C. Klingler
  • Wiland Schmale
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 62)

Abstract

In this paper, we survey a part of feedback stabilization for systems over commutative rings. Since many excellent sources exist which describe the motivation behind the study of systems over rings, we shall not touch on that here. The interested reader is referred to [1], [8], [9], [12], [13], and [14].

Key words

linear systems pole assignability dynamic feedback 

AMS(MOS) subject classifications

93b55 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Brewer, J. Bunce, and F. Van Vleck, Linear Systems Over Commutative Ring, Marcel Dekker, 1986.Google Scholar
  2. 2.
    J. Brewer and L. Klingler, Dynamic feedback over commutative rings, Lin. Alg. and Its Appl., 98, 1988, pp. 137–168.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    J. Brewer, L. Klingler, and W. Schmale, The dynamic feedback cyclization problem for principal ideal domains, to appear.Google Scholar
  4. 4.
    J. Brewer, L Klingler, and W. Schmale, C[y] is a CA-ring and coefficient assignment is properly weaker than feedback cyclization over a p.i.d., to appear.Google Scholar
  5. 5.
    R. Bumby, E. Sontag, H. Sussman, and W. Vasconcelos, Remarks on the pole-shifting problem over rings, J. Pure and Appl. Alg., 2, 1981, pp. 113–127.CrossRefGoogle Scholar
  6. 6.
    E. Emre and P. Khargonekar, Regulation of split linear systems over rings: Coefficient assignment and observers, IEEE Trans. Aut. Control, AC-27, 1982, pp. 104–113.MathSciNetCrossRefGoogle Scholar
  7. 7.
    M. Heymann, Comments on pole assignment in multi-input controllable linear systems, IEEE Trans. Aut Control, AC-13, 1968, pp. 748–749.MathSciNetCrossRefGoogle Scholar
  8. 8.
    E. Kamen, Lectures on algebraic system theory: Linear systems over commutative rings, NASA Contractor Report 3016, 1978.Google Scholar
  9. 9.
    E. Kamen, Linear systems over rings: From R. E. Kaiman to the present, Mathematical System Theory-The Influence of R. E. Kaiman, Springer-Verlag, 1991.Google Scholar
  10. 10.
    W. Schmale, Feedback cyclization over certain principal ideal domains, Int. J. Control, 48, 1988, pp. 89–96.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    W. Schmale, Three-dimensional feedback cyclization over C[T], Systems and Control Letters, 12, 1989, pp. 327–330.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    E. Sontag, Linear systems over commutative rings: a survey, Richerche Automat., 7, 1976, pp. 1–34.Google Scholar
  13. 13.
    E. Sontag, An introduction to the stabilization problem for parameterized families of linear systems, Contemp. Math., 47, 1985, pp. 369–400.MathSciNetGoogle Scholar
  14. 14.
    E. Sontag and Y. Wang, Pole shifting for families of linear systems depending on at most three parameters, Lin. Alg. and Its Appl., 137, 1990, pp. 3–38.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • J. W. Brewer
    • 1
  • L. C. Klingler
    • 1
  • Wiland Schmale
    • 2
  1. 1.Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Department of MathematicsCarl v. Ossietzky Universität OldenburgOldenburgGermany

Personalised recommendations