Xiong, JunlinPetersen, Ian R.Lanzon, Alexander2026-07-032026-07-039788995605691ORCID:/0000-0003-4856-9450/work/219177659https://hdl.handle.net/1885/733812324The 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.This work was supported by the Australian Research Council , and in part by the Engineering and Physical Sciences Research Council , the National Natural Science Foundation of China ( 61004044 ). The material in this paper was partially presented at the Seventh Asian Control Conference, August 27–29, 2009, Hong Kong, China. This paper was recommended for publication in revised form by Associate Editor Tong Zhou under the direction of Editor Roberto Tempo.6en200971449101251