A gap metric perspective of well-posedness for nonlinear feedback interconnections
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4246770
- author
- Khong, Sei Zhen LU ; Cantoni, Michael and Manton, Jonathan H.
- organization
- publishing date
- 2013
- type
- Contribution to conference
- publication status
- published
- subject
- conference name
- 2013 Australian Control Conference
- conference location
- Perth, Australia
- conference dates
- 2013-11-04
- external identifiers
-
- scopus:84893268654
- language
- English
- LU publication?
- yes
- id
- 784d962b-c63a-4657-9618-b0c847da6943 (old id 4246770)
- date added to LUP
- 2016-04-04 13:38:24
- date last changed
- 2022-01-30 00:40:30
@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}},
}