Hurwitz Matrix for Polynomial Matrices

  • F. J. Kraus
  • M. Mansour
  • M. Sebek
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)


If a system is given by its transfer function then the stability of the system is determined by the denominator polynomial and its corresponding Hurwitz matrix H. Also the critical stability conditions are determined by its determinant det H.

The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the Hurwiz matrix for a polynomial and the Lyapunov equation. Here we show how the Hurwitz matrix appears in the solution of the Lyapunov equation using the companion matrix realization and the Kronecker formulation of Lyapunov equation. Using this result we show how the generalized Hurwitz matrix for polynomial matrices can be constructed.


Polynomial Matrix Lyapunov Equation Polynomial Matrice State Space Realisation Hurwitz Matrix 
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Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • F. J. Kraus
    • 1
  • M. Mansour
    • 1
  • M. Sebek
    • 1
  1. 1.Automatic Control LaboratorySwiss Federal Institute of Technology ETH-ZentrumZürichSwitzerland

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