On non-proper negative imaginary systems

This paper studies non-proper negative imaginary systems. First, the concept of negative imaginary transfer functions thatmayhavepoles at the origin and infinity is introduced. Then, a generalized lemma is presented to provide a sufficient condition to characterize the non-proper negative imaginary properties of systems. The generalized lemma is given in terms of complex variable s in the quarter domain of analyticity. Compared to previous results, our result removes the symmetric restriction. Also, a new relationship is established between (lossless) negative imaginary and (lossless) positive real transfer function matrices by using a minor decomposition. The results in this paper give us the possibility to address non-proper and non-symmetric descriptor systemswith negative imaginary frequency response. Several examples are presented to illustrate the results. © 2015 Published by Elsevier B.V.