\begin{tabular}{@{}L{0.25\linewidth}L{0.17\linewidth}L{0.2\linewidth}L{0.29\linewidth}@{}}
\toprule
Gain matrix & eigenvalues of $G^{+}(0)$ & principal submatrices of $-G^{+}(0)$ not D-stable & verdict \\
\midrule
Al-Doura naphtha column, $4\times4$~\cite{MahmoodAlzobai2026} & $1.25$, $1.61$, $17.86\pm3.45i$ & none & totally D-stable; diagonal Lyapunov certificate $P=\diag(2/5,2/5,81/10,4/5)$ (Lean); $\ks=\infty$ \\
same, manipulated inputs $(R,Q_R,F)$ only, $3\times3$ & $0.79$, $1.65$, $23.15$ & none & totally D-stable; diagonal Lyapunov certificate $P=\diag(7/10,4/5,9/5)$; $\ks=\infty$ \\
Elaahi--Luyben sidestream column, $4\times4$~\cite{ElaahiLuyben1985,SkogestadMorari1992} & $-9.69$, $4.74$, $6.05$, $19.88$ & \{1,3\}; \{1,4\}; \{2,4\}; \{3,4\}; \{1,2,3\}; \{1,2,4\}; \{1,3,4\}; \{2,3,4\}; \{1,2,3,4\} & not totally D-stable; every listed submatrix is not even Hurwitz, so $\ks=1$ for it \\
\bottomrule
\end{tabular}