Geometric characterization on the solvability of regulator equations

Xiaohua Xia, Jiangfeng Zhang

Research output: Contribution to journalArticle

1 Citation (Scopus)
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The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained.
Original languageEnglish
Pages (from-to)445-450
Number of pages6
Issue number2
Publication statusPublished - Feb 2008


  • geometric characterization
  • solvability
  • regulator equations
  • friend set
  • left invertibility
  • output regulation
  • regulator equation
  • controlled invariant submanifold

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