Stability analysis of positive feedback interconnections of linear negative imaginary systems

The paper is concerned with the stability analysis of positive feedback interconnections of negative imaginary systems. Firstly, a previously established Negative Imaginary Lemma is shown to remain true even if the transfer function has poles on the imaginary axis. This is achieved by suitably extending the definitions of negative imaginary transfer functions. Secondly, a necessary and sufficient condition is established for the internal stability of the feedback interconnection of negative imaginary systems. Moreover, some properties of negative imaginary transfer functions are developed. Finally, a numerical example is presented to illustrate the theory.