Existence Conditions of H Suboptimal Controllers

  • Ben M. Chen
Part of the Communications and Control Engineering book series (CCE)


The first fundamental issue one faces in an H optimization problem, is when, or under what conditions a γ suboptimal controller exists. Fortunately, the problem regarding the existence conditions of γ-suboptimal controllers for either the regular or singular type of continuous-time or discrete-time systems has almost been completely solved in the literature. As it was mentioned in the introduction, there were four main different approaches developed in early years, which include: 1) Interpolation approach (see e.g., Limbeer and Anderson [77]); 2) Frequency domain approach (see e.g., Doyle [47], Francis [54] and Glover [57]); 3) Polynomial approach (see e.g., Kwakernaak [69]); and 4) J-spectral factorization approach (see e.g., Kimura [67]). All these techniques mainly deal with the regular problem.


Riccati Equation Imaginary Axis Existence Condition Full Column Rank Algebraic Riccati Equation 
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Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Ben M. Chen
    • 1
  1. 1.Department of Electrical EngineeringNational University of SingaporeSingapore

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