Two classes of passive time-varying well-posed linear systems

Roland Schnaubelt*, George Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax-Phillips semigroup induced by a well-posed linear system, as in scattering theory.

Original languageEnglish
Pages (from-to)265-301
Number of pages37
JournalMathematics of Control, Signals, and Systems
Volume21
Issue number4
DOIs
StatePublished - Aug 2010

Keywords

  • Lax-Phillips semigroup
  • Linear time-varying system
  • Operator semigroup
  • Scattering passive system
  • Well-posed linear system

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