Skip to main content
SpringerLink
Log in

Controlled and conditioned invariant subspaces in linear system theory

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kalman, R. E.,On the General Theory of Control Systems, Proceedings of the First IFAC Congress, Vol. 1, Butterworths, London, 1961.

    Google Scholar 

  2. Kalman, R. E.,Canonical Structure of Linear Dynamical Systems, Proceedings of National Academy of Sciences, Vol. 48, 1962.

  3. Kalman, R. E., Ho, Y. C., andNarendra, K. S.,Controllability of Linear Dynamical Systems, Contributions to Differential Equations, Vol. 1, 1962.

  4. Gilbert, E. G.,Controllability and Observability in Multivariable Control Systems, SIAM Journal on Control, Vol. 1, No. 2, 1963.

  5. Kalman, R. E.,Mathematical Description of Linear Dynamical Systems, SIAM Journal on Control, Vol. 1, No. 2, 1963.

  6. Kreindler, E., andSarachik, P. E.,On the Concepts of Controllability and Observability in Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-9, No. 2, 1964.

  7. Weiss, L., Kalman, R. E.,Contributions to Linear System Theory, International Journal of Engineering Science, Vol. 3, No. 2, 1965.

  8. Silverman, L. M., andMeadows, H. E.,Controllability and Observability in Time-Variable Linear Systems, SIAM Journal on Control, Vol. 5, No. 1, 1967.

  9. Basile, G., Laschi, R., andMarro, G.,Luoghi Caratteristici delle Traiettorie dei Sistemi Lineari nello Spazio delle Uscite, L'Elettrotecnica, Vol. 56, No. 5, 1969.

  10. Basile, G., andMarro, G.,On the Observability of Linear Time-Invariant Systems with Unknown Inputs, Journal of Optimization Theory and Applications, Vol. 3, No. 6, 1969.

Download references

Author information

Authors and Affiliations

  1. Institute of Electrotechnics, University of Bari, Bari, Italy

    G. Basile (Professor of Applied Electronics)

  2. Computing and Servomechanism Center, University of Bologna, Bologna, Italy

    G. Marro (Professor of Automatic Control)

Authors
  1. G. Basile
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Marro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Basile, G., Marro, G. Controlled and conditioned invariant subspaces in linear system theory. J Optim Theory Appl 3, 306–315 (1969). https://doi.org/10.1007/BF00931370

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00931370

Keywords

Search

Navigation