  A necessary and sufficient condition, expressed simply as the DC loop gain
(ie the loop gain at zero frequency) being less than unity, is given in this
paper to guarantee the internal stability of a feedback interconnection of
Linear Time-Invariant (LTI) Multiple-Input Multiple-Output (MIMO) systems with
negative imaginary frequency response. Systems with negative imaginary
frequency response arise for example when considering transfer functions from
force actuators to co-located position sensors, and are commonly important in
for example lightly damped structures. The key result presented here has
similar application to the small-gain theorem, which refers to the stability of
feedback interconnections of contractive gain systems, and the passivity
theorem (or more precisely the positive real theorem in the LTI case), which
refers to the stability of feedback interconnections of positive real systems.
A complete state-space characterisation of systems with negative imaginary
frequency response is also given in this paper and also an example that
demonstrates the application of the key result is provided.
