Model reduction by balanced truncation for systems with nuclear Hankel operators

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Abstract

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
Volume52
Issue number2
DOIs
Publication statusPublished - 29 Apr 2014

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Nuclear Operators
Balanced Truncation
Sobolev spaces
Hankel Operator
Model Reduction
Mathematical operators
Convergence Theory
Hankel
Numerical Algorithms
Sobolev Spaces
Lyapunov
Error Bounds
Infinity
Norm
Approximation

Keywords

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

Cite this

Model reduction by balanced truncation for systems with nuclear Hankel operators. / Guiver, Christopher; Opmeer, M.R.

In: SIAM Journal on Control and Optimization, Vol. 52, No. 2, 29.04.2014, p. 1366-1401.

Research output: Contribution to journalArticle

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