Nonlinear H Control Theory: A Literature Survey

  • Joseph A. Ball
  • J. William Helton
Part of the Progress in Systems and Control Theory book series (PSCT, volume 4)


The central problem of H -control theory roughly is to optimize (by the choice of compensator in a standard feedback configuration) some worst case (i.e. infinity norm) measure of performance while maintaining stability. For the linear, time-invariant, finitedimensional case, rather complete state space solutions are now available, and work has begun on understanding less restrictive settings. A recent new development has been the establishment of a connection with differential games and the perception of the H -problem as formally the same as the earlier well established linear quadratic regulator problem, but with an indefinite performance objective. In this article we review the current state of the art for nonlinear systems. The main focus is on the approach through a global theory of nonlinear J-inner-outer factorization and nonlinear fractional transformations being developed by the authors. It turns out that the critical points arising naturally in this theory can also be interpreted as optimal strategies in a game-theoretic interpretation of the control problem.


Internal Stability 27th IEEE Conf Nonlinear Plant Coprime Factorization Infinity Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Joseph A. Ball
    • 1
  • J. William Helton
    • 2
  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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