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Phase-sensitive structured singular value

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Open Problems in Mathematical Systems and Control Theory

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

Given Γ ∈ Cn ×n with Γ + Γ* ≥ 0, define the phase Φ(Γ) of Γ by

$$\Phi \left( \Gamma \right) = {\cot ^{ - 1}}\left( {\sup \left\{ {b:\Gamma + \Gamma * - \frac{\beta }{j}\left( {\Gamma - \Gamma *} \right) \geqslant 0\forall \beta \in \left\{ { - b,\,b} \right\}} \right\}} \right).$$

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References

  1. L. Lee, “Robustness Study of Systems with Phase-Informed Uncertainty,” Ph.D. Dissertation, Department of Electrical Engineering, University of Maryland, College Park, MD 20742, 1992.

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  2. A. L. Tits, V. Balakrishnan, and L. Lee, “Robustness Under Bounded Uncertainty with Phase Information,” to appear in IEEE Trans. Automatic Control, November 1998.

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  3. E. G. Eszter and C. V. Hollot, “An IQC for Uncertainty Satisfying Both Norm-bounded and Passivity Constraints,” Automatica, 33 (8), pp. 1545–1548 (1997).

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  4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, volume 15 of Studies in Applied Mathematics. SIAM, Philadelphia, PA, June 1994.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Institute for Systems Research, University of Maryland, College Park, MD, 20742, USA

    André L. Tits

  2. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907-1285, USA

    V. Balakrishnan

Authors
  1. André L. Tits
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  2. V. Balakrishnan
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Leige, Sart Tilman B37, B-4000, Liege, Belgium

    Vincent Blondel (PhD) (PhD)

  2. Department of Mathematics, Rutgers University, Hill Center 724, 08903, New Brunswick, USA

    Eduardo D. Sontag (PhD) (PhD)

  3. Centre for Arificial Intelligence and Robotics, Raj Bhavan Cirlce - High Grounds, 560001, Bangalore, India

    Mathukumalli Vidyasagar (PhD) (PhD)

  4. Institute of Mathematics, Rijksuniversiteit te Groningen, Postbus 800, 9700, Av Groningen, The Netherlands

    Jan C. Willems (PhD) (PhD)

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© 1999 Springer-Verlag London Limited

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Tits, A.L., Balakrishnan, V. (1999). Phase-sensitive structured singular value. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_42

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  • DOI: https://doi.org/10.1007/978-1-4471-0807-8_42

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1207-5

  • Online ISBN: 978-1-4471-0807-8

  • eBook Packages: Springer Book Archive

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