Mathematics of Control, Signals and Systems

, Volume 7, Issue 4, pp 306–330 | Cite as

Embedding of time-varying contractive systems in lossless realizations

  • Alle -Jan van der Veen
  • Patrick Dewilde
Article
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Abstract

The lossless embedding problem, also known as the Darlington synthesis or unitary extension problem, considers the extension of a given contractive system to become the partial input-output operator of a lossless system. In this paper the embedding problem is solved for discrete-time time-varying systems with finite but possibly time-varying state dimensions, for the strictly contractive as well as the boundary case. The construction is done in a state space context and gives rise to a time-varying Riccati difference equation which is shown to have a closed-form solution. As a corollary, a discrete-time Bounded Real Lemma is formulated, linking contractiveness of an input-output operator to conditions on its state realization.

Key words

Lossless embedding Linear time-varying systems Riccati difference equation Bounded real lemma 
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Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Alle -Jan van der Veen
    • 1
  • Patrick Dewilde
    • 1
  1. 1.Department of Electrical EngineeringDelft University of TechnologyCD DelftThe Netherlands

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