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LMI Approach to Robust Control

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Encyclopedia of Systems and Control

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Abstract

In the analysis and design of robust control systems, LMI method plays a fundamental role. This article gives a brief introduction to this topic. After the introduction of LMI, it is illustrated how a control design problem is related with matrix inequality. Then, two methods are explained on how to transform a control problem characterized by matrix inequalities to LMIs, which is the core of the LMI approach. Based on these knowledge, the LMI solutions to various kinds of robust control problems are illustrated. Included are \(\mathcal{H}_{\infty }\) and \(\mathcal{H}_{2}\) control, regional pole placement, and gain-scheduled control.

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Bibliography

  • Apkarian P, Gahinet P (1995) A convex characterization of gain-scheduled \(\mathcal{H}_{\infty }\) controllers. IEEE Trans Autom Control 40(5):853–864

    Article  MATH  MathSciNet  Google Scholar 

  • Boyd SP et al (1994) Linear matrix inequalities in system and control. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Chilali M, Gahinet P (1996) H ∞ design with pole placement constraints: an LMI approach. IEEE Trans Autom Control 41(3):358–367

    Article  MATH  MathSciNet  Google Scholar 

  • Chilali M, Gahinet P, Apkarian P (1999) Robust pole placement in LMI regions. IEEE Trans Autom Control 44(12):2257–2270

    Article  MATH  MathSciNet  Google Scholar 

  • Gahinet P (1996) Explicit controller formulas for LMI-based \(\mathcal{H}_{\infty }\) synthesis. Automatica 32(7):1007–1014

    Article  MATH  MathSciNet  Google Scholar 

  • Gahinet P, Apkarian P (1994) A linear matrix inequality approach to \(\mathcal{H}_{\infty }\) control. Int J Robust Nonlinear Control 4:421–448

    Article  MATH  MathSciNet  Google Scholar 

  • Gahinet P, Nemirovski A, Laub AJ, Chilali M (1995) LMI control toolbox. The MathWorks, Inc., Natick

    Google Scholar 

  • Liu KZ, Yao Y (2014, to appear) Robust control: theory and applications. Wiley, New York

    Google Scholar 

  • Nesterov Y, Nemirovskii A (1994) Interior-point polynomial methods in convex programming. SIAM, Philadelphia

    Book  Google Scholar 

  • Packard A (1994) Gain scheduling via linear fractional transformations. Syst Control Lett 22: 79–92

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, 263-8522, Chiba, Japan

    Ph.D. Kang-Zhi Liu

Authors
  1. Ph.D. Kang-Zhi Liu
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Correspondence to Kang-Zhi Liu .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Liu, KZ. (2013). LMI Approach to Robust Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_161-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_161-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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