Direct and indirect couplings in coherent feedback control of linear quantum systems

Guofeng Zhang, Matthew R. James

Research output: Journal article publicationJournal articleAcademic researchpeer-review

121 Citations (Scopus)


The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent H∞and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.
Original languageEnglish
Article number5648449
Pages (from-to)1535-1550
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number7
Publication statusPublished - 1 Jul 2011
Externally publishedYes


  • Coherent feedback
  • dissipation
  • gain
  • H control ∞
  • LQG control
  • passivity
  • quantum feedback control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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