Skip to main content

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

  • Conference paper
  • First Online:
Book cover Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1029))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. WONHAM: On pole assignment in multi-input controllable linear systems IEEE Trans. AC 12 (1967), 660–665.

    Article  Google Scholar 

  2. C. BYRNES: Stabilizability of multivariable systems and the Ljusternik-Snirel’man category of real grassmannians, preprint 1981.

    Google Scholar 

  3. J.C. WILLEMS: The LQG-problem: a brief tutorial introduction. In [34] 29–44.

    Google Scholar 

  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. 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, 125–193

    Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  7. R.E. KALMAN. P.L. Falb. M.A. Arbib, Topics in mathematical system theory, Mac Graw-Hill, 1969.

    Google Scholar 

  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. A. LINDQUIST-G. PICCI: State space models for gaussian stochastic processes. In [34], 141–168.

    Google Scholar 

  10. M. HAZEWINKEL: Moduli and canonical forms for linear dynamical systems II: the topological case, Math. Syst. Th. 10 (1977), 363–385.

    Article  MathSciNet  MATH  Google Scholar 

  11. C. BYRNES: On the control of certain deterministic infinite dimensional systems by algebro-geometric techniques, Amer J. Math. 100 (1978), 1333–1381

    Article  MathSciNet  MATH  Google Scholar 

  12. A. TANNEMBAUM: Invariance and system theory, Lect. Notes Math. 845, Springer, 1981.

    Google Scholar 

  13. V. DLAB-P. GABRIEL (eds): Representation theory I, II, Lect. Notes Math. 831, 832, Springer, 1981.

    Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. HARPER-G.C. ROTA: Matching theory: an introduction. In: P. Ney (ed.), Adv. in Probability, Vol. 1, Marcel Dekker, 1971, 171–215.

    MathSciNet  MATH  Google Scholar 

  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. E. RUCH: The diagram lattice as structural principle. Theor. Chim. Acta 38 (1975), 167–183.

    Article  MathSciNet  Google Scholar 

  19. E. RUCH-A. MEAD: The principle of increasing mixing character and some of its consequences, Theor. Chim. Acta 41 (1976), 95–117.

    Article  Google Scholar 

  20. P.M. ALBERTI-A. UHLMANN: Stochasticity and partial order, Reidel, 1982.

    Google Scholar 

  21. M. HAZEWINKEL-C.F. MARTIN: On decentralization, symmetry and special structure in linear systems, submitted J. Pure and Appl. Algebra.

    Google Scholar 

  22. M. HAZEWINKEL-S.I. MARCUS: On Lie algebras and finite dimensional filtering. Stochastics 7 (1982), 29–62.

    Article  MathSciNet  MATH  Google Scholar 

  23. R.W. BROCKETT: Non-linear systems and non-linear estimation theory. In [34], 441–478.

    Google Scholar 

  24. S. K. MITTER, Non-linear filtering ans stochastic mechanics. In [34], 479–504.

    Google Scholar 

  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. H.J. SUSSMANN: Rigorous results on the cubic sensor problem, In [34], 637–648.

    Google Scholar 

  27. M. HAZEWINKEL: On deformation, approximations and non-linear filtering, Systems and control letters 1 (1981), 32–36.

    Article  MathSciNet  MATH  Google Scholar 

  28. H.J. SUSSMAN: Approximate finite dimensional filters for some non-linear problems, Systems and Control letters, to appear.

    Google Scholar 

  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. M. HAZEWINKEL: The linear systems Lie algebra, the Segal-Shale-Weil representation and all Kalman-Bucy filters, Subm. Amer. J. Math.

    Google Scholar 

  31. D. SHALE: Linear symmetries of free boson fields. Trans. Amer. Math. Soc. 103 (1962), 149–167.

    Article  MathSciNet  MATH  Google Scholar 

  32. I.E. SEGAL: Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand 13 (1963), 31–43.

    MathSciNet  MATH  Google Scholar 

  33. A. WEIL: Sur certains groupes d’opérateurs unitaires. Coll. works Vol.III 1–71, Springer, 1980.

    MATH  Google Scholar 

  34. M. HAZEWINKEL-J.C. WILLEMS (eds.), Stochastic systems: the mathematics of filtering and identification and applications, Reidel, 1981.

    Google Scholar 

  35. M. HAZEWINKEL-C.F. Martin: Symmetric linear systems: an application of algebraic system theory, submitted IEEE Trans. AC.

    Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marie-Paule Malliavin

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Hazewinkel, M. (1983). Lectures on invariants, representations and lie algebras in systems and control theory. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098925

Download citation

  • DOI: https://doi.org/10.1007/BFb0098925

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12699-7

  • Online ISBN: 978-3-540-38686-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics