Robust performance analysis for uncertain negative-imaginary systems

Zhuoyue Song, Alexander Lanzon, Sourav Patra, Ian R. Petersen

    Research output: Contribution to journalArticlepeer-review


    Negative-imaginary systems are important in engineering practice as this class of systems appears quite often in practical problems, for example, lightly damped flexible structures with collocated position sensors and force actuators. In this paper, an analytical framework for robust performance of uncertain negative-imaginary systems is proposed. The results are obtained by transforming negative-imaginary systems into a bounded-real framework via the positive-real property. This paper deals with all the significant technical difficulties that appear due to the transformation and the punctured j ω-axis frequency condition of negative-imaginary systems. The problem is equivalently cast into a structured singular value condition that gives a quantitative performance test for this class of systems. This result also gives an analytical framework for robust stability when the perturbations are mixture of bounded-real and negative-imaginary uncertainties. A numerical example is presented to show the usefulness of the proposed methods. © 2011 John Wiley & Sons, Ltd.
    Original languageEnglish
    Pages (from-to)262-281
    Number of pages19
    JournalInternational Journal of Robust and Nonlinear Control
    Issue number3
    Publication statusPublished - Feb 2012


    • bounded-real
    • H ∞ control
    • lightly damped systems
    • negative-imaginary systems
    • positive-real
    • robust performance
    • structured singular value


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