On lossless negative imaginary systems

Junlin Xiong, Ian R. Petersen, Alexander Lanzon

    Research output: Contribution to journalArticlepeer-review


    The paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback. Firstly, the concept of lossless negative imaginary transfer functions is introduced and some properties of such 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 provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller. Finally, a flexible structure example is presented to illustrate the theory. © 2012 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1213-1217
    Number of pages4
    Issue number6
    Publication statusPublished - Jun 2012


    • Linear systems
    • Lossless negative imaginary systems
    • Stability


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