  This paper provides a state feedback stabilization approach for nonlinear
systems of relative degree less than or equal to two by rendering them
nonlinear negative imaginary (NI) systems. Conditions are provided under which
a nonlinear system can be made a nonlinear NI system or a nonlinear output
strictly negative imaginary (OSNI) system. Roughly speaking, an affine
nonlinear system that has a normal form with relative degree less than or equal
to two, after possible output transformation, can be rendered nonlinear NI and
nonlinear OSNI. In addition, if the internal dynamics of the normal form are
input-to-state stable, then there exists a state feedback input that stabilizes
the system. This stabilization result is then extended to achieve stability for
systems with a nonlinear NI uncertainty.
