Passive linear discrete-time systems: Characterization through structure

Research output: Contribution to journalArticlepeer-review


We here show that the family of finite-dimensional, discrete-time, passive, linear time-invariant systems can be characterized through the structure of a matrix-convex set, which is maximal in the sense of being closed under products of its elements Moreover, this observation unifies three setups: (i) difference inclusions, (ii) matrix-valued rational functions, (iii) realization arrays associated with rational functions. It turns out that in the continuous-time case the corresponding structure is of a maximal matrix-convex cone closed under inversion.

Original languageEnglish
Pages (from-to)299-315
Number of pages17
JournalLinear Algebra and Its Applications
StatePublished - 15 Aug 2021


  • Discrete-time bounded real rational functions
  • Kalman-Yakubovich-Popov lemma
  • Matrix-convex sets
  • Passive linear systems
  • State-space realization

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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