Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

  • Elizabeth Rita SamuelEmail author
  • Luc Knockaert
  • Tom Dhaene
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 325)


A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. The direct parameterization of poles and residues may be not appropriate, due to their possible non-smooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the pole-residue description to a Sylvester description which is computed for each root macromodel. This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester technique for parametric macromodeling.


Sylvester equation Parametric macromodel State-space matrices Interpolation 



This research has been funded by the Research Foundation Flanders (FWO) and the Interuniversity Attraction Poles Programme BESTCOM initiated by the Belgian Science Policy Office.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Elizabeth Rita Samuel
    • 1
    Email author
  • Luc Knockaert
    • 1
  • Tom Dhaene
    • 1
  1. 1.Ghent University—IMindsGentBelgium

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