S-Lemma with Equality and Its Applications

Yong Xia, Shu Wang, Ruey-Lin Sheu

Let $f(x)=x^{T}Ax+2a^{T}x+c$ and $h(x)=x^{T}Bx+2b^{T}x+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the sys…