Automation and Remote Control

, Volume 69, Issue 11, pp 1932–1945 | Cite as

Petersen’s lemma on matrix uncertainty and its generalizations

  • M. V. Khlebnikov
  • P. S. Shcherbakov
Adaptive and Robust Systems


Various generalizations and refinements are proposed for a well-known result on robust matrix sign-definiteness, which is extensively exploited in quadratic stability, design of robustly quadratically stabilizing controllers, robust LQR-problem, etc. The main emphasis is put on formulating the results in terms of linear matrix inequalities.

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • M. V. Khlebnikov
    • 1
  • P. S. Shcherbakov
    • 1
  1. 1.Trapesnikov Institute of Control ScienceRussian Academy of SciencesMoscowRussia

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