Stability analysis of interconnected systems with mixed negative-imaginary and small-gain properties

Sourav Patra, Alexander Lanzon

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this letter, an analytical framework is proposed to examine stability of two stable, linear time invariant systems interconnected in positive feedback where the systems have mixed properties of negative-imaginary and small-gain. Using the notion of dissipativity, the interconnection of systems is guaranteed to be finite-gain stable under the condition that the dc loop gain is contractive. This work builds on Griggs, and exploits a new set of frequency dependent triplets that was introduced in above reference to mix two unconditional stability statements, i.e., small-gain and passivity. Unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative-imaginary systems are connected in a feedback loop can be mixed with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop. The usefulness of the proposed analytical framework is demonstrated via a numerical example. © 2006 IEEE.
    Original languageEnglish
    Article number5723702
    Pages (from-to)1395-1400
    Number of pages5
    JournalIEEE Transactions on Automatic Control
    Volume56
    Issue number6
    DOIs
    Publication statusPublished - Jun 2011

    Keywords

    • Bounded-real system
    • dissipativeness
    • finite-gain stability
    • interconnected system
    • negative-imaginary system
    • positive feedback

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