A common problem in the context of linear parameter-
varying (LPV) systems is how input-output (IO) models can
be efficiently realized in terms of state-space (SS) representations.
The problem originates from the fact that in the LPV literature
discrete-time identification and modeling of LPV systems is often
accomplished via IO model structures. However, to utilize these
LPV-IO models for control synthesis, commonly it is required
to transform them into an equivalent SS form. In general, such
a transformation is complicated due to the phenomenon of dynamic
dependence (dependence of the resulting representation on
time-shifted versions of the scheduling signal). This conversion
problem is revisited and practically applicable approaches are
suggested which result in discrete-time SS representations that
have only static dependence (dependence on the instantaneous
value of the scheduling signal). To circumvent complexity, a criterion
is also established to decide when an linear-time invariant
(LTI)-type of realization approach can be used without introducing
significant approximation error. To reduce the order of
the resulting SS realization, an LPV Ho-Kalman-type of model
reduction approach is introduced, which, besides its simplicity,
is capable of reducing even non-stable plants. The proposed
approaches are illustrated by application oriented examples.