μ-Analysis and synthesis based on parameter dependent multipliers

  • Gan Chen
  • Toshiharu Sugie
Part D Robust Control
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)


It is well known that the structured singular value μ plays a crucial role in analysis and synthesis of the systems having structured uncertainties. In this paper, first, we propose new upper bounds of μ based on the parameter dependent multipliers, which are less conservative than former ones. Second, using this type of multipliers, we give a necessary and sufficient condition for dynamical systems to have μ less than a specified value γ for every frequency, which requires neither frequency sweep nor higher order multipliers. Third, based on this result, we solve a state feedback μ synthesis problem via LMI’s. Numerical examples demonstrate the effectiveness of the proposed method.


State Feedback Synthesis Problem Small Gain Theorem Bilinear Matrix Inequality Suboptimal Controller 
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

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Gan Chen
    • 1
  • Toshiharu Sugie
    • 2
  1. 1.Comp. & Sys. Sci. Eng.Osaka Prefecture UniversitySakai, OsakaJapan
  2. 2.Dept. of Applied Systems ScienceKyoto UniversityUji, KyotoJapan

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