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Structured and Simultaneous Lyapunov Functions for System Stability Problems

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Robustness in Identification and Control

Part of the book series: Applied Information Technology ((AITE))

Abstract

It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of x = Ax for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given. Proofs can be found in Boyd and Yang [BY88].

Research sponsored in part by ONR under N00014-86-K-0112, NSF under ECS-85-52465, an IBM faculty development award, and Bell Communications Research.

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Author information

Authors and Affiliations

  1. Electrical Engineering Department, Stanford University, Stanford, CA, 94305, USA

    Stephen Boyd & Qinping Yang

Authors
  1. Stephen Boyd
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  2. Qinping Yang
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Editor information

Editors and Affiliations

  1. Turin Polytechnic, Turin, Italy

    M. Milanese  & R. Tempo  & 

  2. University of Florence, Florence, Italy

    A. Vicino

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© 1989 Plenum Press, New York

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Boyd, S., Yang, Q. (1989). Structured and Simultaneous Lyapunov Functions for System Stability Problems. In: Milanese, M., Tempo, R., Vicino, A. (eds) Robustness in Identification and Control. Applied Information Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9552-6_16

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  • DOI: https://doi.org/10.1007/978-1-4615-9552-6_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9554-0

  • Online ISBN: 978-1-4615-9552-6

  • eBook Packages: Springer Book Archive

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