Decay of Hankel singular values of analytic control systems

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We show that control systems with an analytic semigroup and control and observation operators that are not too unbounded have a Hankel operator that belongs to the Schatten class S-p for all positive p. This implies that the Hankel singular values converge to zero faster than any polynomial rate. This in turn implies fast convergence of balanced truncations. As a corollary, decay rates for the eigenvalues of the controllability and observability Gramians are also provided. Applications to the heat equation and a plate equation are given.
Original languageEnglish
Pages (from-to)635-638
Number of pages4
JournalSystems & Control Letters
Issue number10
Early online date16 Aug 2010
Publication statusPublished - Oct 2010


  • model order reduction
  • infinite-dimensional systems
  • Hankel operator


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