On the topology of the space of reachable symmetric linear systems

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


Canonical Form Positive Real Number Homotopy Type Orbit Space Cell Decomposition 
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  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

  1. 1.Department of MathematicsPedagogical Institute of VINHViet Nam

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