Some Equivalent Results with Yakubovich's $S$-Lemma

Authors:
Yan Zi-zong;Guo Jin-hai
Affiliations:
zzyan@yangtzeu.edu.cn and xin3fei@21cn.com;-
Venue:
SIAM Journal on Control and Optimization
Year:
2010

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Abstract

This paper presents an elementary proof of nonstrict Finsler's theorem and discusses five closely related theorems: Yakubovich's $S$-lemma, Yuan's alternative theorem, nonstrict Finsler's theorem, strict Finsler's theorem, and Finsler-Calabi's theorem. This paper discusses how one is related with another. At the end of this article we present some extensions of these results to an infinite-dimensional vector space.