= Drag-polynomial stability for all positive stopping rates
{title2=$K\geq L\geq P>0,\quad K>P$}
Consider the real family $s^4+2\gamma s^3+(K+\gamma^2)s^2+2L\gamma s+P\gamma^2$ with fixed $K,L,P$. The <Routh-Hurwitz criterion> reduces its nontrivial determinant to $4\gamma^2[L(K-L)+\gamma^2(L-P)]$. Strict decay for every finite $\gamma>0$ is equivalent to the displayed inequalities: the constant and slope must be nonnegative, with at least one positive, and coefficient positivity requires $P>0$. The stricter chain $K>L>P>0$ is sufficient but excludes valid equality cases. Neither equality case guarantees a uniform decay margin as $\gamma$ tends to zero or infinity. At $\gamma=0$ there is no asymptotic attraction.
Back to article page
