A New Stability Result for the Feedback Interconnection of Negative   Imaginary Systems with a Pole at the Origin
  This paper is concerned with stability conditions for the positive feedback interconnection of negative imaginary systems. A generalization of the negative imaginary lemma is derived, which remains true even if the transfer function has poles on the imaginary axis including the origin. A sufficient condition for the internal stability of a feedback interconnection for NI systems including a pole at the origin is given and an illustrative example is presented to support the result. 
Mohamed A. Mabrok, Abhijit G. Kallapur, Ian R. Petersen, and Alexander   Lanzon
math.OC cs.SY