  In this study, we extend the theory of negative imaginary (NI) systems to a
nonlinear framework using a frequency-domain approach. The extended notion is
completely characterized via a finite-frequency integration over a "kernel
function" on energy-bounded input and output signal pairs. The notion is
closely related to and carefully contrasted with the well-studied extension of
negative imaginariness -- the theory of counterclockwise dynamics. A condition
for feedback stability of the proposed nonlinear NI systems is then developed
based on the technique of integral quadratic constraints. Examples and
simulations on feedback interconnections of typical nonlinear systems are
provided to demonstrate the effectiveness.
