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Structured Singular Value and Applications: Analyzing the Effect of Linear Time-Invariant Uncertainty in Linear Systems

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Encyclopedia of Systems and Control

Abstract

This entry presents the most commonly used formulations of robust stability and robust \(\mathcal{H}_{\infty }\) performance for linear systems with highly structured, linear, time-invariant uncertainty. The structured singular value function (μ) is specifically defined for this purpose, involving a problem-specific set, called the uncertainty set. With the uncertainty set chosen, μ is a real-valued function defined on complex matrices of a fixed dimension. A few key properties are easily derived from the definition and then applied to solve the robustness analysis problem. Computation of μ, which is required to implement the analysis tests, is difficult, so computable and refinable upper and lower bounds are derived.

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Author information

Authors and Affiliations

  1. Mechanical Engineering, University of California, Berkeley, USA

    Andrew Packard

  2. Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

    Pete Seiler

  3. Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

    Gary Balas

Authors
  1. Andrew Packard
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  2. Pete Seiler
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  3. Gary Balas
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Corresponding author

Correspondence to Andrew Packard .

Editor information

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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© 2014 Springer-Verlag London

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Packard, A., Seiler, P., Balas, G. (2014). Structured Singular Value and Applications: Analyzing the Effect of Linear Time-Invariant Uncertainty in Linear Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_163-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_163-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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