 Drag-polynomial stability for all positive stopping rates

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.