A spectral test for observability and reachability of time-varying systems

M. A. Peters, Pablo A Iglesias

Research output: Contribution to journalArticle


A spectral test for the observability and reachability of linear time-invariant systemsthe Popov-Belevitch-Hautus test-is well known and serves as a powerful characterization of these properties. In this paper it is shown that similar tests exist for linear time-varying systems. The test presented here involves a check over a subset of the spectrum of the weighted block shift known as the set of almost eigenvalues.

Original languageEnglish (US)
Pages (from-to)1330-1345
Number of pages16
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 1999



  • Controllability
  • Discrete-time systems
  • Exponential stability
  • Observability
  • Operator-theoretic methods
  • Time-varying systems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

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