Circuits, Systems and Signal Processing

, Volume 8, Issue 3, pp 357–373 | Cite as

Infinite elementary divisors of polynomial matrices and impulsive solutions of linear homogeneous matrix differential equations

  • A. I. G. Vardulakis
  • G. Fragulis


Impulsive solutions of linear homogeneous matrix differential equations are re-examined in the light of the theory of Jordan chains that correspond to infinite elementary divisors of the associated polynomial matrix. Infinite elementary divisors of general polynomial matrices are defined and their relation to the pole-zero structure of polynomial matrices at infinity is examined. It is shown that impulsive solutions are due to Jordan chains of a “dual” polynomial matrix that correspond to infinite elementary divisors that are associated with the orders of “zeros at infinity” of the original matrix.


Differential Equation Polynomial Matrix Original Matrix Elementary Divisor Homogeneous Matrix 


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Copyright information

© Birkhäuser Boston Inc. 1989

Authors and Affiliations

  • A. I. G. Vardulakis
    • 1
  • G. Fragulis
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesAristotle University of ThessalonikiThessalonikiGreece

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