Controlled and conditioned invariant subspaces in linear system theory

  • G. Basile
  • G. Marro
Contributed Papers

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.

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References

  1. 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. 2.
    Kalman, R. E.,Canonical Structure of Linear Dynamical Systems, Proceedings of National Academy of Sciences, Vol. 48, 1962.Google Scholar
  3. 3.
    Kalman, R. E., Ho, Y. C., andNarendra, K. S.,Controllability of Linear Dynamical Systems, Contributions to Differential Equations, Vol. 1, 1962.Google Scholar
  4. 4.
    Gilbert, E. G.,Controllability and Observability in Multivariable Control Systems, SIAM Journal on Control, Vol. 1, No. 2, 1963.Google Scholar
  5. 5.
    Kalman, R. E.,Mathematical Description of Linear Dynamical Systems, SIAM Journal on Control, Vol. 1, No. 2, 1963.Google Scholar
  6. 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.Google Scholar
  7. 7.
    Weiss, L., Kalman, R. E.,Contributions to Linear System Theory, International Journal of Engineering Science, Vol. 3, No. 2, 1965.Google Scholar
  8. 8.
    Silverman, L. M., andMeadows, H. E.,Controllability and Observability in Time-Variable Linear Systems, SIAM Journal on Control, Vol. 5, No. 1, 1967.Google Scholar
  9. 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.Google Scholar
  10. 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.Google Scholar

Copyright information

© Plenum Publishing Corporation 1969

Authors and Affiliations

  • G. Basile
    • 1
  • G. Marro
    • 2
  1. 1.Institute of ElectrotechnicsUniversity of BariBariItaly
  2. 2.Computing and Servomechanism CenterUniversity of BolognaBolognaItaly

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