  We report a systematic study of the C(2)$^1\Pi_u$ electronic state in
rubidium dimer, observed in polarization labelling spectroscopy experiment
through the C $\leftarrow$ X$^{1}\Sigma^{+}_{g}$ transitions recorded under
rotational resolution in two isotopologues $^{85}$Rb$_2$ and
$^{85}$Rb$^{87}$Rb. Regularity of the vibrational progressions was distorted by
numerous interactions with the surrounding 2$^1\Sigma^{+}_{\mathrm{u}}$,
2$^3\Pi_{\mathrm{u}}$ and 3$^3\Sigma^{+}_{\mathrm{u}}$ states. Deperturbation
was performed by coupled-channels analysis taking into account spin-orbit and
rotational interactions. Potential energy curves and parameters describing the
off-diagonal matrix elements were determined as functions of internuclear
distance. About 3000 line frequencies from the present study are reproduced
with a standard deviation of 0.07 cm$^{-1}$, in agreement with the experimental
accuracy. Along with this, the model is consistent with all high resolution
experimental data on the involved electronic states, available in the
literature.
