J-spectral factorization approach to H control

Michael Green, Keith Glover, David Limebeer, John Doyle

Research output: Contribution to journalArticlepeer-review

169 Citations (Scopus)


Necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with H control are derived using J-spectral factorization theory. The existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled J-spectral factorization problems, with the second factor providing a parametrization of all solutions to the model matching problem. The existence of the J-spectral factors is then shown to be equivalent to the existence of nonnegative definite, stabilizing solutions to two indefinite algebraic Riccati equations, allowing a state-space formula for a linear fractional representation of all controllers to be given. A virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework, and no additional auxiliary Riccati equations are required.

Original languageEnglish
Pages (from-to)1350-1371
Number of pages22
JournalSIAM Journal on Control and Optimization
Issue number6
Publication statusPublished - 1990
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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