  This paper considers the Lurye system of a discrete-time, linear
time-invariant plant in negative feedback with a nonlinearity. Both monotone
and slope-restricted nonlinearities are considered. The main result is a
procedure to construct destabilizing nonlinearities for the Lurye system. If
the plant satisfies a certain phase condition then a monotone nonlinearity can
be constructed so that the Lurye system has a non-trivial periodic cycle.
Several examples are provided to demonstrate the construction. This represents
a contribution for absolute stability analysis since the constructed
nonlinearity provides a less conservative upper bound than existing bounds in
the literature.
