A "mixed" small gain and passivity theorem in the frequency domain

Wynita M. Griggs, Brian D O Anderson, Alexander Lanzon

    Research output: Contribution to journalArticlepeer-review


    We show that the negative feedback interconnection of two causal, stable, linear time-invariant systems, with a "mixed" small gain and passivity property, is guaranteed to be finite-gain stable. This "mixed" small gain and passivity property refers to the characteristic that, at a particular frequency, systems in the feedback interconnection are either both "input and output strictly passive"; or both have "gain less than one"; or are both "input and output strictly passive" and simultaneously both have "gain less than one". The "mixed" small gain and passivity property is described mathematically using the notion of dissipativity of systems, and finite-gain stability of the interconnection is proven via a stability result for dissipative interconnected systems. © 2007 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)596-602
    Number of pages6
    JournalSystems and Control Letters
    Issue number9-10
    Publication statusPublished - Sept 2007


    • Dissipative systems
    • Finite gain
    • Linear systems
    • Passivity
    • Stability


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