Matrix notation question (in reference to "simultaneous interconnection and damping assignment passivity based control"):
We select an $n\times n$ matrix called $F_d(x)$. Let $G(x) := F_d(x)+F_d(x)^T$ under the constraint that the following inequality holds: $G(x) < 0$.
My Question: Does this mean that each element in $G(x)$ must be less than zero, or just the eigenvalues of $G(x)$ must be less than zero?
From my general memory of control system, it usually means negative definite, i.e. all eigenvalues are negative. Usually, it uses the symbol $ \prec$ some books just used $<$... depending on the convention.
https://en.wikipedia.org/wiki/Definite_matrix#Notation