Skip to main content
SpringerLink
Log in
Book cover

Invariant Subspaces and Other Topics pp 163–179Cite as

Birkhäuser

Control Subspaces of Minimal Dimension, and Spectral Multiplicities

  • Chapter

  • 197 Accesses

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 6))

Abstract

Let us consider a linear dynamical system

$$\dot{x}(t)=Ax(t)+Bu(t),:\ t\geq 0$$
((*))

where A: X→X, B: U→X are bounded linear operators, X (the state space) and U (the control or input space) are some normed linear spaces.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Васюнин, В.И.; Никольский, H.К.: Управляющие подпространства минимальной размерности. Элементарное введение. Discotheca, Записки научн. семинаров ЛОМИ, Ленинград, 113(1981), 41–75.

    Google Scholar 

  2. Васюнин, В.И.; Никольский, Н.К.: Управляющие подпространства минимальной размерности. Влияние корневых векторов. Discotheca, Препринт ЛОМИ, P-4-81,Ленинград, 1981, 1-45.

    Google Scholar 

  3. Васюнин, В.И.; Никольский, Н.К.: Управляющие подпространства минимальной размерности. Унитарные и модельные операторы. Discotheca, Препринт ЛОМИ, P-5-81, Ленинград, 1981.

    Google Scholar 

  4. Никольский, H.К.: Лекции об операторе сдвига, Москва, “Наука”, 1980.

    Google Scholar 

  5. Feintuch, A: On single input controllability for infinite dimensional linear systems, J. Math. Anal. Appl. 62 (1978), 538–546.

    Article  Google Scholar 

  6. Heymann, M.: On the input and output reducibility of multivariable linear systems, IEEE Trans. Aut. Control AC-15(1970), 563–569.

    Article  Google Scholar 

  7. Sarason, D.: Weak-star density of polynomials, J. Reine Angew. Math. 252 (1972), 1–15.

    Google Scholar 

  8. Wermer, J.: On invariant subspaces of normal operators, Proc. Amer. Math. Soc. 3 (1952), 270–277.

    Article  Google Scholar 

  9. Wermer, J.: On restrictions of operators, Proc. Amer. Math. Soc. 4 (1953), 860–865.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 191011, Leningrad, Fontanka 27, LOMI, USSR

    N. K. Nikolskii & V. I. Vasjunin

Authors
  1. N. K. Nikolskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Vasjunin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, INCREST, Bd. Pǎcii 220, 79622, Bucharest, Romania

    C. Apostol , R. G. Douglas , B. Sz.-Nagy  & D. Voiculescu , ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer Basel AG

About this chapter

Cite this chapter

Nikolskii, N.K., Vasjunin, V.I. (1982). Control Subspaces of Minimal Dimension, and Spectral Multiplicities. In: Apostol, C., Douglas, R.G., Sz.-Nagy, B., Voiculescu, D., Arsene, G. (eds) Invariant Subspaces and Other Topics. Operator Theory: Advances and Applications, vol 6. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5445-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5445-0_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5447-4

  • Online ISBN: 978-3-0348-5445-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation