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Lectures on invariants, representations and lie algebras in systems and control theory

  • Michiel Hazewinkel
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1029)

Keywords

Vector Bundle Symmetric Group Symmetry Algebra Linear Dynamical System Grassmann Manifold 
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References

  1. [1]
    M. WONHAM: On pole assignment in multi-input controllable linear systems IEEE Trans. AC 12 (1967), 660–665.CrossRefGoogle Scholar
  2. [2]
    C. BYRNES: Stabilizability of multivariable systems and the Ljusternik-Snirel’man category of real grassmannians, preprint 1981.Google Scholar
  3. [3]
    J.C. WILLEMS: The LQG-problem: a brief tutorial introduction. In [34] 29–44.Google Scholar
  4. [4]
    M. HAZEWINKEL: On families of linear systems: degeneration phenomena. In C. Byrnes, C.F. Martin (eds), Linear system theory, AMS, 1980, 157–190.Google Scholar
  5. [5]
    M. HAZEWINKEL: (Fine) moduli (spaces) for linear systems: what they are and what they are good for, In: C. Byrnes, C.F. Martin (eds), Geometric methods for the theory of linear systems, Reidel, 1980, 125–193Google Scholar
  6. [6]
    M. HAZEWINKEL: A partial survey of the uses of algebraic geometry in systems and control theory. In: Symposia Math. INDAM. 24, Acad. Press, 1981. 245–292.MathSciNetzbMATHGoogle Scholar
  7. [7]
    R.E. KALMAN. P.L. Falb. M.A. Arbib, Topics in mathematical system theory, Mac Graw-Hill, 1969.Google Scholar
  8. [8]
    M. HAZEWINKEL: On the (internal) symmetry group of linear dynamical systems. In P. Kramer, M. Dal Cin (eds), Groups, systems and many-body physics, Vieweg, 1980, 362–404.Google Scholar
  9. [9]
    A. LINDQUIST-G. PICCI: State space models for gaussian stochastic processes. In [34], 141–168.Google Scholar
  10. [10]
    M. HAZEWINKEL: Moduli and canonical forms for linear dynamical systems II: the topological case, Math. Syst. Th. 10 (1977), 363–385.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    C. BYRNES: On the control of certain deterministic infinite dimensional systems by algebro-geometric techniques, Amer J. Math. 100 (1978), 1333–1381MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    A. TANNEMBAUM: Invariance and system theory, Lect. Notes Math. 845, Springer, 1981.Google Scholar
  13. [13]
    V. DLAB-P. GABRIEL (eds): Representation theory I, II, Lect. Notes Math. 831, 832, Springer, 1981.Google Scholar
  14. [14]
    M. HAZEWINKEL-C.F. MARTIN: A short elementary proof of Grothendieck’s theorem on algebraic vectorbundles over the projective line, J. pure and appl. Algebra 25 (1982), 207–212.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    M. HAZEWINKEL, A.C.F. Vorst, On the Snapper, Lübler-Vidale, Lam theorem on permutation representations of the symmetric groups, J. pure and appl. Algebra 23 (1982), 29–32.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    L. HARPER-G.C. ROTA: Matching theory: an introduction. In: P. Ney (ed.), Adv. in Probability, Vol. 1, Marcel Dekker, 1971, 171–215.MathSciNetzbMATHGoogle Scholar
  17. [17]
    M. HAZEWINKEL-C. F. MARTIN: Representations of the symmetric group, the specialization order, systems and Grassmann manifolds, to appear Ens. Math.Google Scholar
  18. [18]
    E. RUCH: The diagram lattice as structural principle. Theor. Chim. Acta 38 (1975), 167–183.MathSciNetCrossRefGoogle Scholar
  19. [19]
    E. RUCH-A. MEAD: The principle of increasing mixing character and some of its consequences, Theor. Chim. Acta 41 (1976), 95–117.CrossRefGoogle Scholar
  20. [20]
    P.M. ALBERTI-A. UHLMANN: Stochasticity and partial order, Reidel, 1982.Google Scholar
  21. [21]
    M. HAZEWINKEL-C.F. MARTIN: On decentralization, symmetry and special structure in linear systems, submitted J. Pure and Appl. Algebra.Google Scholar
  22. [22]
    M. HAZEWINKEL-S.I. MARCUS: On Lie algebras and finite dimensional filtering. Stochastics 7 (1982), 29–62.MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    R.W. BROCKETT: Non-linear systems and non-linear estimation theory. In [34], 441–478.Google Scholar
  24. [24]
    S. K. MITTER, Non-linear filtering ans stochastic mechanics. In [34], 479–504.Google Scholar
  25. [25]
    M. HAZEWINKEL-S.I. MARCUS-H.J. SUSSMANN: Non existence of finite dimensional filters for conditional statistics of the cubic sensor problem, preprint, 1982.Google Scholar
  26. [26]
    H.J. SUSSMANN: Rigorous results on the cubic sensor problem, In [34], 637–648.Google Scholar
  27. [27]
    M. HAZEWINKEL: On deformation, approximations and non-linear filtering, Systems and control letters 1 (1981), 32–36.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    H.J. SUSSMAN: Approximate finite dimensional filters for some non-linear problems, Systems and Control letters, to appear.Google Scholar
  29. [29]
    B. HANZON-M. HAZEWINKEL: On identification of linear systems and the estimation Lie algebra of the associated non-linear filtering problem. In: Proc. 6-th IFAC Conf. on Identification, Washington, June 1982.Google Scholar
  30. [30]
    M. HAZEWINKEL: The linear systems Lie algebra, the Segal-Shale-Weil representation and all Kalman-Bucy filters, Subm. Amer. J. Math.Google Scholar
  31. [31]
    D. SHALE: Linear symmetries of free boson fields. Trans. Amer. Math. Soc. 103 (1962), 149–167.MathSciNetzbMATHCrossRefGoogle Scholar
  32. [32]
    I.E. SEGAL: Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand 13 (1963), 31–43.MathSciNetzbMATHGoogle Scholar
  33. [33]
    A. WEIL: Sur certains groupes d’opérateurs unitaires. Coll. works Vol.III 1–71, Springer, 1980.zbMATHGoogle Scholar
  34. [34]
    M. HAZEWINKEL-J.C. WILLEMS (eds.), Stochastic systems: the mathematics of filtering and identification and applications, Reidel, 1981.Google Scholar
  35. [35]
    M. HAZEWINKEL-C.F. Martin: Symmetric linear systems: an application of algebraic system theory, submitted IEEE Trans. AC.Google Scholar
  36. [36]
    J.C. WILLEMS: Almost invariant subspaces: an approach to high gain feedback design, I, II, IEEE Trans. AC 26 (1981), 235–252, ibid to appear.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Michiel Hazewinkel
    • 1
  1. 1.The Math. CentreAmsterdam

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