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Robust Stabilization for Parametric Uncertainty with Application to Magnetic Levitation

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Robust Control Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 66))

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Abstract

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 2m 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.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering for Computer-Controlled Machinery, Osaka University, Suita, Osaka, 565, Japan

    Shigeru Yamamoto & Hidenori Kimura

Authors
  1. Shigeru Yamamoto
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  2. Hidenori Kimura
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    Bruce A. Francis

  2. Department of Electrical Engineering and Computer Science, University of Michigan, 48109, Ann Arbor, MI, USA

    Pramod P. Khargonekar

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© 1995 Springer-Verlag New York, Inc.

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Yamamoto, S., Kimura, H. (1995). Robust Stabilization for Parametric Uncertainty with Application to Magnetic Levitation. In: Francis, B.A., Khargonekar, P.P. (eds) Robust Control Theory. The IMA Volumes in Mathematics and its Applications, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8451-9_7

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  • DOI: https://doi.org/10.1007/978-1-4613-8451-9_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8453-3

  • Online ISBN: 978-1-4613-8451-9

  • eBook Packages: Springer Book Archive

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