Robust Stabilization for Parametric Uncertainty with Application to Magnetic Levitation

  • Shigeru Yamamoto
  • Hidenori Kimura
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 66)


This paper considers the quadratic stabilization for a class of uncertain linear systems. The system under consideration contains norm-bounded time-varying uncertainties. The quadratic stability problem for the system is reduced to finding a common positive definite solution of 2 m Lyapunov equations, where m is the number of uncertain scalar parameters. A sufficient condition for the quadratic stabilizability of uncertain systems is derived in terms of a Riccati equation containing at most 2(m + 1) free parameters. The results are applied to the stabilizing control of a magnetic levitation system. The effectiveness of our method is illustrated both in simulations and experiments.

Key words

quadratic stability quadratic stabilization Riccati equation magnetic levitation 


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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Shigeru Yamamoto
    • 1
  • Hidenori Kimura
    • 1
  1. 1.Department of Mechanical Engineering for Computer-Controlled MachineryOsaka UniversitySuita, Osaka, 565Japan

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