  The paper makes the first steps towards a behavioral theory of LPV
state-space representations with an affine dependency on scheduling, by
characterizing minimality of such state-space representations. It is shown that
minimality is equivalent to observability, and that minimal realizations of the
same behavior are isomorphic.Finally, we establish a formal relationship
between minimality of LPV state-space representations with an affine dependence
on scheduling and minimality of LPV state-space representations with a dynamic
and meromorphic dependence on scheduling.
