A gap metric perspective of wellposedness 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 closedloop operators is also investigated. It is established that if a certain openloop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closedloop... (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 closedloop operators is also investigated. It is established that if a certain openloop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closedloop operator is causal provided the latter is weakly additive. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4246770
 author
 Khong, Sei Zhen; Cantoni, Michael and Manton, Jonathan H.
 organization
 publishing date
 2013
 type
 Contribution to conference
 publication status
 published
 subject
 conference name
 2013 Australian Control Conference
 external identifiers

 Scopus:84893268654
 language
 English
 LU publication?
 yes
 id
 784d962bc63a46579618b0c847da6943 (old id 4246770)
 date added to LUP
 20140214 12:50:49
 date last changed
 20161013 04:56:37
@misc{784d962bc63a46579618b0c847da6943, 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 closedloop operators is also investigated. It is established that if a certain openloop mapping has an inverse over signals with arbitrary start time (i.e. zero before some initial time), then the closedloop 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 wellposedness for nonlinear feedback interconnections}, year = {2013}, }