Optimal Hankel Norm Model Reduction by Truncation of Trajectories

B. Roorda, S. Weiland

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We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.
Original languageEnglish
Place of PublicationTilburg
Number of pages6
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper


  • Optimal Hankel norm approximation
  • Balancing
  • Linear systems
  • l2-systems
  • Faddeev sequences


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