Model reduction by balanced truncation for systems with nuclear Hankel operators

Christopher Guiver, M.R. Opmeer

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We prove the H-infinity error bounds for Lyapunov balanced truncation and for optimal Hankel norm approximation under the assumption that the Hankel operator is nuclear. This is an improvement of the result from Glover, Curtain, and Partington [SIAM J. Control Optim., 26(1998), pp. 863-898], where additional assumptions were made. The proof is based on convergence of the Schmidt pairs of the Hankel operator in a Sobolev space. We also give an application of this convergence theory to a numerical algorithm for model reduction by balanced truncation.
Original languageEnglish
Pages (from-to)1366-1401
Number of pages36
JournalSIAM Journal on Control and Optimization
Issue number2
Early online date29 Apr 2014
Publication statusPublished - 31 Dec 2014


  • infinite-dimensional system
  • model reduction
  • Hankel operator
  • realization
  • balanced realization
  • optimal Hankel norm approximation


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