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

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

doi:10.1016/j.sysconle.2007.04.005

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

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

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	596-602
Number of pages	6
Journal	Systems and Control Letters
Volume	56
Issue number	9-10
DOIs	https://doi.org/10.1016/j.sysconle.2007.04.005
Publication status	Published - Sept 2007

Keywords

Dissipative systems
Finite gain
Linear systems
Passivity
Stability

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10.1016/j.sysconle.2007.04.005

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abstract = "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. {\textcopyright} 2007 Elsevier B.V. All rights reserved.",

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author = "Griggs, {Wynita M.} and Anderson, {Brian D O} and Alexander Lanzon",

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language = "English",

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TY - JOUR

T1 - A "mixed" small gain and passivity theorem in the frequency domain

AU - Griggs, Wynita M.

AU - Anderson, Brian D O

AU - Lanzon, Alexander

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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.

KW - Dissipative systems

KW - Finite gain

KW - Linear systems

KW - Passivity

KW - Stability

U2 - 10.1016/j.sysconle.2007.04.005

DO - 10.1016/j.sysconle.2007.04.005

M3 - Article

SN - 0167-6911

VL - 56

SP - 596

EP - 602

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 9-10

ER -

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

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Keywords

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