  This paper introduces a systematic approach to synthesize linear
parameter-varying (LPV) representations of nonlinear (NL) systems which are
described by input affine state-space (SS) representations. The conversion
approach results in LPV-SS representations in the observable canonical form.
Based on the relative degree concept, first the SS description of a given NL
representation is transformed to a normal form. In the SISO case, all
nonlinearities of the original system are embedded into one NL function, which
is factorized, based on a proposed algorithm, to construct an LPV
representation of the original NL system. The overall procedure yields an LPV
model in which the scheduling variable depends on the inputs and outputs of the
system and their derivatives, achieving a practically applicable transformation
of the model in case of low order derivatives. In addition, if the states of
the NL model can be measured or estimated, then a modified procedure is
proposed to provide LPV models scheduled by these states. Examples are included
to demonstrate both approaches.
