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Infinite elementary divisors of polynomial matrices and impulsive solutions of linear homogeneous matrix differential equations. (English) Zbl 0678.34002
Summary: 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.

MSC:
34A99 General theory for ordinary differential equations
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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