The eigenstructure of an arbitrary polynomial matrix : Computational aspects

Van Dooren, Paul;Dewilde, P.
(1983) Linear Algebra and Its Applications — Vol. 50, p. 545-580 (1983)

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Authors
  • Van Dooren, PaulUCLouvain
    Author
  • Dewilde, P.TU Delft
    Author
Abstract
We give a new numerical method to compute the eigenstructure—i.e. the zero structure, the polar structure, and the left and right null space structure—of a polynomial matrix P(λ). These structural elements are of fundamental importance in several systems and control problems involving polynomial matrices. The approach is more general than previous numerical methods because it can be applied to an arbitrary m × n polynomial matrix P(λ) with normal rank r smaller than m and/or n. The algorithm is then shown to compute the structure of the left and right null spaces of P(λ) as well. The speed and accuracy of this new approach are also discussed.
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Van Dooren, P., & Dewilde, P. (1983). The eigenstructure of an arbitrary polynomial matrix : Computational aspects. Linear Algebra and Its Applications, 50, 545-580. https://doi.org/10.1016/0024-3795(83)90069-1 (Original work published 1983)