  After reviewing commutativity of second-order linear time-varying analog
systems, the inverse commutativity conditions are derived for these systems by
considering non-zero initial conditions. On the base of these conditions, the
transitivity property is studied for second order linear time-varying unrelaxed
analog systems. It is proven that this property is always valid for such
systems when their initial states are zero; when non-zero initial states are
present, it is shown that the validity of transitivity does not require any
more conditions and it is still valid. Throughout the study it is assumed that
the subsystems considered can not be obtained from each other by any
feed-forward and feed-back structure. The results are well validated by MATLAB
simulations.
