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A gap metric perspective of well-posedness for nonlinear feedback interconnections

Khong, Sei Zhen LU ; Cantoni, Michael and Manton, Jonathan H. (2013) 2013 Australian Control Conference
Abstract
A differential geometric approach based on the gap metric is taken to examine the uniqueness of solutions of the equations describing a feedback interconnection. It is shown that under sufficiently small perturbations on the Fréchet derivative of a nonlinear plant as measured by the gap metric, the uniqueness property is preserved if solutions exist given exogenous signals. The results developed relate the uniqueness of solutions for a nominal feedback interconnection and that involving the derivative of the plant. Causality of closed-loop operators is also investigated. It is established that if a certain open-loop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closed-loop... (More)
A differential geometric approach based on the gap metric is taken to examine the uniqueness of solutions of the equations describing a feedback interconnection. It is shown that under sufficiently small perturbations on the Fréchet derivative of a nonlinear plant as measured by the gap metric, the uniqueness property is preserved if solutions exist given exogenous signals. The results developed relate the uniqueness of solutions for a nominal feedback interconnection and that involving the derivative of the plant. Causality of closed-loop operators is also investigated. It is established that if a certain open-loop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closed-loop operator is causal provided the latter is weakly additive. (Less)
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Contribution to conference
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conference name
2013 Australian Control Conference
external identifiers
  • Scopus:84893268654
language
English
LU publication?
yes
id
784d962b-c63a-4657-9618-b0c847da6943 (old id 4246770)
date added to LUP
2014-02-14 12:50:49
date last changed
2017-01-01 08:13:22
@misc{784d962b-c63a-4657-9618-b0c847da6943,
  abstract     = {A differential geometric approach based on the gap metric is taken to examine the uniqueness of solutions of the equations describing a feedback interconnection. It is shown that under sufficiently small perturbations on the Fréchet derivative of a nonlinear plant as measured by the gap metric, the uniqueness property is preserved if solutions exist given exogenous signals. The results developed relate the uniqueness of solutions for a nominal feedback interconnection and that involving the derivative of the plant. Causality of closed-loop operators is also investigated. It is established that if a certain open-loop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closed-loop operator is causal provided the latter is weakly additive.},
  author       = {Khong, Sei Zhen and Cantoni, Michael and Manton, Jonathan H.},
  language     = {eng},
  title        = {A gap metric perspective of well-posedness for nonlinear feedback interconnections},
  year         = {2013},
}