Hurwitz stable matrix
= Hurwitz stable matrix
{c}
{title2=$\operatorname{Re}\lambda(A)<0$}
A Hurwitz stable matrix has all eigenvalues strictly in the open left half-plane. For $\dot x=Ax$, this is equivalent to $e^{At}x\to0$ for every initial vector. <Jordan blocks> contribute polynomial factors times $e^{\lambda t}$, which decay exactly when their eigenvalues have negative real part. Translating an affine equilibrium reduces its attractivity to this same condition.