An entropy formula for time-varying discrete-time control systems

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of the W-transform which generalizes the usual Z-transform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that arise in time-varying H control, there exists a unique, bounded contraction which maximizes the entropy. This generalizes known results in the time-invariant case. Possible extensions are discussed, along with state-space formulae.

Original languageEnglish (US)
Pages (from-to)1691-1706
Number of pages16
JournalSIAM Journal on Control and Optimization
Issue number5
StatePublished - Sep 1996


  • Optimal control
  • Spectral factorizations
  • Time-varying systems

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


Dive into the research topics of 'An entropy formula for time-varying discrete-time control systems'. Together they form a unique fingerprint.

Cite this