Balancing of Lossless and Passive Systems

Arjan van der Schaft

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10 Citations (Scopus)
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Different balancing techniques are applied to lossless nonlinear systems, with open-loop balancing applied to their scattering representation. It is shown that they all lead to the same result: the pair of to-be-balanced functions is given by two copies of the physical energy function, yielding thus no information about the relative importance of the state components in a balanced realization. In particular, in the linear lossless case all balancing singular values and similarity invariants are equal to one. This result is extended to general passive systems, in which case the to-be-balanced functions are ordered into a single sequence of inequalities, and the similarity invariants are all less than or equal to one.
Original languageEnglish
Pages (from-to)2153-2157
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - Oct-2008


  • Balancing
  • lossless
  • nonlinear
  • passive
  • scattering

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