A negative-imaginary lemma without minimality assumptions and robust state-feedback synthesis for uncertain negative-imaginary systems

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

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Negative-imaginary systems have important engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators. This paper proposes a new Negative-Imaginary Lemma for generalized negative-imaginary systems, where the minimality assumption is relaxed. The proposed lemma facilitates both analysis and synthesis for negative-imaginary systems. Invoking this result, a systematic robust static state-feedback synthesis method is proposed in an LMI framework for systems with strictly negative-imaginary uncertainty (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure) assuming all states are available for state feedback. Two numerical examples are given to show the usefulness of the proposed results. © 2012 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)1269-1276
    Number of pages7
    JournalSystems and Control Letters
    Volume61
    Issue number12
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Lightly damped systems
    • Negative-imaginary systems
    • Passivity
    • Robust control

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