Robust Stability Analysis for Feedback Interconnections of TimeVarying Linear Systems
(2013) In SIAM Journal on Control and Optimization 51(1). p.353379 Abstract
 Feedback interconnections of causal linear systems are studied in a continuoustime setting. The developments include a linear timevarying (LTV) generalization of Vinnicombe's nugap metric and an integralquadraticconstraintbased robust L2stability theorem for uncertain feedback interconnections of potentially openloop unstable systems. These main results are established in terms of ToeplitzWienerHopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 inputoutput pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties... (More)
 Feedback interconnections of causal linear systems are studied in a continuoustime setting. The developments include a linear timevarying (LTV) generalization of Vinnicombe's nugap metric and an integralquadraticconstraintbased robust L2stability theorem for uncertain feedback interconnections of potentially openloop unstable systems. These main results are established in terms of ToeplitzWienerHopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 inputoutput pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV statespace models to initially motivate the abstract formulation, and subsequently verified for frequencydomain multiplication by constantly proper CallierDesoer transfer functions in analysis that confirms consistency of the developments with the timeinvariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributedparameter systems over a network with timevarying gains. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4246727
 author
 Cantoni, Michael; Jönsson, Ulf T. and Khong, Sei Zhen ^{LU}
 publishing date
 2013
 type
 Contribution to journal
 publication status
 published
 subject
 in
 SIAM Journal on Control and Optimization
 volume
 51
 issue
 1
 pages
 353  379
 external identifiers

 Scopus:84876109660
 language
 English
 LU publication?
 no
 id
 3c9d0bf0b851471e90e7568b75a2f409 (old id 4246727)
 date added to LUP
 20140214 12:41:42
 date last changed
 20161013 05:01:56
@misc{3c9d0bf0b851471e90e7568b75a2f409, abstract = {Feedback interconnections of causal linear systems are studied in a continuoustime setting. The developments include a linear timevarying (LTV) generalization of Vinnicombe's nugap metric and an integralquadraticconstraintbased robust L2stability theorem for uncertain feedback interconnections of potentially openloop unstable systems. These main results are established in terms of ToeplitzWienerHopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 inputoutput pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV statespace models to initially motivate the abstract formulation, and subsequently verified for frequencydomain multiplication by constantly proper CallierDesoer transfer functions in analysis that confirms consistency of the developments with the timeinvariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributedparameter systems over a network with timevarying gains.}, author = {Cantoni, Michael and Jönsson, Ulf T. and Khong, Sei Zhen}, language = {eng}, number = {1}, pages = {353379}, series = {SIAM Journal on Control and Optimization}, title = {Robust Stability Analysis for Feedback Interconnections of TimeVarying Linear Systems}, volume = {51}, year = {2013}, }