Interconnections of nonlinear systems with "mixed" small gain and passivity properties and associated input-output stability results

Wynita M. Griggs, Brian D O Anderson, Alexander Lanzon, Michael C. Rotkowitz

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A negative feedback interconnection consisting of two causal, nonlinear systems is shown to be input-output stable when a "mixed" small gain and passivity assumption is placed on each of the systems. The "mixed" small gain and passivity property captures the well-known notions of passivity and small gain associated with systems: the property can be appropriately reduced to an input and output strictly passive system description; or alternatively, can be reduced to a description of a system with small gain. More importantly, the property captures the concept of a "blending" of the small gain and passivity ideas. This concept of "blending" can be visualized, for example, by considering linear time-invariant systems that exhibit passivity-type properties at, say, low frequencies; and lose these passivity-type properties but have small gain at high frequencies. © 2008 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)289-295
    Number of pages6
    JournalSystems and Control Letters
    Volume58
    Issue number4
    DOIs
    Publication statusPublished - Apr 2009

    Keywords

    • Finite gain
    • Input-output stability
    • Nonlinear systems
    • Passivity

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