A "mixed" small gain and passivity theorem in the frequency domain
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Griggs, Wynita; Anderson, Brian; Lanzon, Alexander
Description
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...[Show more]
dc.contributor.author | Griggs, Wynita | |
---|---|---|
dc.contributor.author | Anderson, Brian | |
dc.contributor.author | Lanzon, Alexander | |
dc.date.accessioned | 2015-12-07T22:53:47Z | |
dc.identifier.issn | 0167-6911 | |
dc.identifier.uri | http://hdl.handle.net/1885/27876 | |
dc.description.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. | |
dc.publisher | Elsevier | |
dc.source | Systems and Control Letters | |
dc.subject | Keywords: Dissipativity; Finite gain; Finite-gain stability; Frequency domain analysis; Linear systems; Stability; Theorem proving; Time varying control systems Dissipative systems; Finite gain; Linear systems; Passivity; Stability | |
dc.title | A "mixed" small gain and passivity theorem in the frequency domain | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 56 | |
dc.date.issued | 2007 | |
local.identifier.absfor | 010203 - Calculus of Variations, Systems Theory and Control Theory | |
local.identifier.ariespublication | u4334215xPUB54 | |
local.type.status | Published Version | |
local.contributor.affiliation | Griggs, Wynita, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Anderson, Brian, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Lanzon, Alexander, University of Manchester | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 596 | |
local.bibliographicCitation.lastpage | 602 | |
local.identifier.doi | 10.1016/j.sysconle.2007.04.005 | |
dc.date.updated | 2015-12-07T12:42:52Z | |
local.identifier.scopusID | 2-s2.0-34447574955 | |
Collections | ANU Research Publications |
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