control system - is the gain positive or negative?
It all depends on the numerator phase angle. This is either \$\small\phi =atan\:(\frac{-\omega}{\omega_{1}})=-90^o\$, or \$\small \phi =atan\:(\frac{\omega}{-\omega_{1}})=90^o\$, as \$\small\omega\rightarrow \infty \$. The denominator phase angle will always be \$\small -270^o\$, as \$\small\omega\rightarrow \infty \$.