The inverse problem of analytic interpolation with degree constraint and weight selection for control synthesis

Johan Karlsson, Tryphon T. Georgiou, Anders G. Lindquist

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The minimizers of certain weighted entropy functionals are the solutions to an analytic interpolation problem with a degree constraint, and all solutions to this interpolation problem arise in this way by a suitable choice of weights. Selecting appropriate weights is pertinent to feedback control synthesis, where interpolants represent closed-loop transfer functions. In this paper we consider the correspondence between weights and interpolants in order to systematize feedback control synthesis with a constraint on the degree. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. This leads to a new procedure for feedback control synthesis.

Original languageEnglish (US)
Article number5378470
Pages (from-to)405-418
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2010

Bibliographical note

Funding Information:
Manuscript received November 23, 2008; revised April 22, 2009. First published January 12, 2010; current version published February 10, 2010. This work was supported by the Swedish Foundation for Strategic Research, the Swedish Research Council, the Göran Gustafsson Foundation, the National Science Foundation, and the Air Force Office of Scientific Research. Recommended by Associate Editor M. Fujita.


  • Analytic interpolation
  • Controller synthesis
  • Degree constraint
  • Loop shaping
  • Model reduction
  • Robust control
  • Weight selection


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