Theoretical analysis demonstrates generalizations of Petersen's lemma in uncertain dynamical systems, suggesting broader applications using linear matrix inequalities.
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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Khlebnikov et al. (2008) studied this question.
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