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On the topology of the space of reachable symmetric linear systems

  • Nguyen Huynh Phàn
Homotopy Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1474)

Keywords

Canonical Form Positive Real Number Homotopy Type Orbit Space Cell Decomposition 
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References

  1. [1]
    M. Aigner: Combinatorial theory. Grundlehren der Math. Wissenschaften 234, Springer 1979.Google Scholar
  2. [2]
    G. Birkhoff and Maclane: A survey of modern algebra. Macmillan, New York, 4th edition 1977.zbMATHGoogle Scholar
  3. [3]
    A. Borel and A. Haefliger: La classe d'homologie fondamentale d'un espace analytique. Bull. Soc. Math. France, 89, 461–513 1961.MathSciNetzbMATHGoogle Scholar
  4. [4]
    R. Brockett: Some geometric questions in theory of linear systems. IEEE Trans. Autom. Control AC-21, 449–455, 1976.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    A. Dold: Lectures on algebraic topology. Springer-Verlage, Berlin Heidelberg, New York, 1972.CrossRefzbMATHGoogle Scholar
  6. [6]
    J. Dieudonné: Foundations of modern analysis. Vol. 3, Academic Press, New York, 1972.Google Scholar
  7. [7]
    U. Helmke: Zur topologie des Raumes linearer Kontrollsysteme. Ph. D. Thesis, Report 100, Forschungsschwerpunkt Dynamische Systeme, University of Bremen, West Germany, 1982.Google Scholar
  8. [8]
    U. Helmke and D. Hinrichsen: Canonical forms and orbit spaces of linear systems. IMA Journal of Mathematical Control and Information, 3, 167–184, 1986.CrossRefzbMATHGoogle Scholar
  9. [9]
    D. Hinrichsen: Metrical and topological aspects of linear control theory. Syst. Anal. Model. Simul. 4, 13–36, 1987.MathSciNetzbMATHGoogle Scholar
  10. [10]
    D. Hinrichsen and D. Prätzel-Wolters: Generalized Hermite matrices and complete invariants of (strict) system equivalence. SIAM J. Control and Optimazation 21, 289–305, 1983.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    D. Hinrichsen, D. Salamon, A. J. Pritchard, P. E. Crouch and e.a.: Introduction to mathematical system theory. Lecture Notes for a Join Cource at the Univerities of Warwick and Bremen, 1980.Google Scholar
  12. [12]
    R. E. Kalman, P. L. Falb and M. A. Arbib: Topics in mathematical system theory. McGraw-Hill, New York, 1969.zbMATHGoogle Scholar
  13. [13]
    W. S. Massey: Homology and cohomology theory. Marcel Dekker, New York, 1978.zbMATHGoogle Scholar
  14. [14]
    J. McCleary: User's guide to spectral sequences. Publish or Perish, Inc. Wilming, Delaware (U.S.A.), 1985.zbMATHGoogle Scholar
  15. [15]
    J. Milnor and J. Stasheff: Characteristic classes. Princeton University Press, 1974.Google Scholar
  16. [16]
    N. H. Phan: Topo cùa không gian các hê thõng tuyen tính dói xúng. TAP CHI TOAN HOC, Vol XV, No 1, 26–31, 1987, (in Vietnamese).Google Scholar
  17. [17]
    N. H. Phan and L. C. Dung: On the topology of the space of reachable observable symmetric linear systems. To appear in the Report Series of Forschungsschwerpunkt Dynamische Systeme, University of Bremen, West Germany.Google Scholar
  18. [18]
    V. M. Popov: Invariant description of linear time-invariant controllable systems. SIAM J. Control, 10, 252–264, 1972.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    E. H. Spanier: Algebraic topology. McGraw-Hill, New York, 1966.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Nguyen Huynh Phàn
    • 1
  1. 1.Department of MathematicsPedagogical Institute of VINHViet Nam

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