There are several types of characterisations of the so-called relative
degree for time-invariant input output systems. Well known concepts for
relative degree exist for time-varying linear and nonlinear systems. This
diploma thesis gives a generalised definition of relative degree for
time-varying nonlinear systems. This definition is used to establish a
characterisation of relative degree for time-varying linear systems in
terms of the time-varying system matrices and their derivatives. It will be
proved that if time-invariant linear systems are considered, then the
description for time-varying linear systems results in the well known
characterisation of relative degree for time-invariant linear systems, and,
if the time-varying linear system is interpreted as time-invariant
nonlinear system, then the definition of relative degree is assured.The
main result of this work is, that the characterisation of relative degree
for time-varying linear systems will be used to derive a normal form for
this systems concerning time-varying linear coordinate transformation.
These normal form is similar to the normal form of time-invariant linear
systems.Finally the normal form for time-varying linear systems is used to
consider the so-called zero dynamics of this systems. Boundedness and
stability for the zero dynamics will be defined and it will be shown that a
time-varying linear system has bounded zero dynamics if, and only if, the
zero dynamics of the corresponding normal form are bounded.