  We formulate a Kalman-style realization theory for discrete-time affine LPV
systems. By an affine LPV system we mean an LPV system whose matrices are
affine functions of the scheduling parameter. In this paper we characterize
those input-output behaviors which exactly correspond to affine LPV systems. In
addition, we characterize minimal affine LPV systems which realize a given
input-output behavior. Furthermore, we explain the relationship between
Markov-parameters, Hankel-matrices, existence of an affine LPV realization and
minimality. The results are derived by reducing the problem to the realization
problem for linear switched systems. In this way, as a secondary contribution,
we formally demonstrate the close relationship between LPV systems and linear
switched systems. In addition we show that an input-output map has a
realization by an affine LPV system if and only if it satisfies certain types
of input-output equations.
