On the Hankel-norm approximation of linear stochastic systems

Andrea Gombani, Michele Pavon

Research output: Contribution to journalArticlepeer-review


We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.

Original languageEnglish (US)
Pages (from-to)283-288
Number of pages6
JournalSystems and Control Letters
Issue number5
StatePublished - Apr 1985


  • Hankel matrices
  • Hankel-norm approximation
  • Linear stochastic systems
  • Singular values
  • Spectral factors

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


Dive into the research topics of 'On the Hankel-norm approximation of linear stochastic systems'. Together they form a unique fingerprint.

Cite this