A Stability Result for Interconnections of Nonlinear Systems with "Mixed" Small Gain and Passivity Properties

Date

2007

Authors

Griggs, Wynita
Anderson, Brian
Lanzon, Alexander
Rotkowitz, Michael

Journal Title

Journal ISSN

Volume Title

Publisher

Institute of Electrical and Electronics Engineers (IEEE Inc)

Abstract

A feedback interconnection consisting of two 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, finite gain. More importantly, the property captures a concept of "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 passivetype properties at, say low frequencies; and lose these passivetype properties but have small gain at high frequencies.

Description

Keywords

Keywords: Interconnection networks; Natural frequencies; Nonlinear systems; Passivity assumption; Time-invariant systems; Asymptotic stability

Citation

Source

Proceedings of the 46th IEEE Conference on Decision and Control 2007

Type

Conference paper

Book Title

Entity type

Access Statement

License Rights

Restricted until

2037-12-31