The Hurwitz Matrix and the Computation of second-order Information Indices

  • Alessandro Beghi
  • Antonio Lepschy
  • Umberto Viaro
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)


An all-pole transfer function Q(s) = 1/P(s), where P(s) is a monic Hurwitz polynomial of degree n, is uniquely characterized by the energies (second-order information indices) of q(t) = LT −1{Q(s)} and of its first n — 1 derivatives. These can be obtained by solving a set of linear equations whose coefficients matrix is the standard Hurwitz matrix for P(s) or by using the entries of its Routh table. Any strictly proper transfer function W(s) = N(s)/P(s) is characterized by n first-order information indices, e.g., Markov parameters, and by n second-order information indices, e.g., the energies of the related impulse response and its n — 1 successive derivatives; these are simply obtainable from the energies of q(t). This fact can be exploited to construct reduced-order models that retain both first- and second-order information indices of a given original system. The extension of this approach to multi-input multi-output systems described by a matrix fraction is analysed.


Impulse Response Model Reduction Information Index Lyapunov Equation Hurwitz Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • Alessandro Beghi
    • 1
  • Antonio Lepschy
    • 1
  • Umberto Viaro
    • 1
  1. 1.Department of Electronics and InformaticsUniversity of PadovaPadovaItaly

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