  Let S be a closed orientable surface of genus at least 2 and let G be a
semisimple real algebraic group of non-compact type. We consider a class of
representations from the fundamental group of S to G called positively ratioed
representations. These are Anosov representations with the additional condition
that certain associated cross ratios satisfy a positivity property. Examples of
such representations include Hitchin representations and maximal
representations. Using geodesic currents, we show that the corresponding length
functions for these positively ratioed representations are well-behaved. In
particular, we prove a systolic inequality that holds for all such positively
ratioed representations.
