Uncertainty bounds for gramian-based interaction measures

  • Authors:

  • Björn Halvarsson;Miguel Castaño;Wolfgang Birk

  • Affiliations:

  • Uppsala University, Dept. of Information Technology, Uppsala, Sweden;Luleå University of Technology, Dept. of Comp. Sci. and Elect. Eng., Luleå, Sweden;Luleå University of Technology, Dept. of Comp. Sci. and Elect. Eng., Luleå, Sweden

  • Venue:
  • ICS'10 Proceedings of the 14th WSEAS international conference on Systems: part of the 14th WSEAS CSCC multiconference - Volume II
  • Year:
  • 2010

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Abstract

Bounds of two Gramian-based Interaction Measures (IM:s) induced by model uncertainty are presented in this paper. The connection between the considered IM:s (the Hankel Interaction Index Array (HIIA) and the Participation Matrix (PM)) is explored, showing that it is possible in certain cases to translate the bounds of one into bounds of the other. The first method is a tightening of previously suggested uncertainty bounds for the HIIA. The second method is based on a novel exploration of the relationship between the PM and the area enclosed by the Nyquist diagram. The latter method is a numerical approximation of the analytical bounds of the PM, whilst the former one provides very loose bounds for the examples presented here.