On lossless negative imaginary systems

The paper is concerned with the notion of lossless negative imaginary systems and their stabilization using a strictly negative imaginary controller through positive feedback. Firstly, some properties of lossless negative imaginary transfer functions are studied. Secondly, a lossless negative imaginary lemma is given which establishes conditions on matrices appearing in a minimal state-space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary. Thirdly, a necessary and sufficient condition is developed for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller. Finally, a numerical example is presented to illustrate the theory.