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
N1 - Funding Information:
This work was supported by ARC Discovery-Projects Grants (DP0342683, DP0664427) and National ICT Australia. National ICT Australia is funded through the Australian Government's Backing Australia's Ability initiative, in part through the Australian Research Council.
Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
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.
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.
KW - Dissipative systems
KW - Finite gain
KW - Linear systems
KW - Passivity
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=34447574955&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2007.04.005
DO - 10.1016/j.sysconle.2007.04.005
M3 - Article
AN - SCOPUS:34447574955
SN - 0167-6911
VL - 56
SP - 596
EP - 602
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 9-10
ER -