Orthogonal embeddings of linear time-varying systems

Research output: Contribution to journalArticlepeer-review


Given a contractive linear system T which is represented as a causal linear contractive operator on a Hilbert space H, we study the question: When does there exist an isometric or unitary causal extension of T to H ⊕H? Here causality is formulated as a lower triangularity condition and we assume the same causality structure for the extension. This question is often referred to as the generalized Darlington synthesis problem for linear time-varying systems.

Original languageEnglish
Pages (from-to)26-43
Number of pages18
JournalMathematics of Control, Signals, and Systems
Issue number1
StatePublished - 1 Jan 2003


  • Causal linear systems
  • Darlington synthesis
  • Isometric dilations
  • Nest algebras
  • Time-varying linear
  • Unitary dilations

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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