Advanced

Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems

Cantoni, Michael; Jönsson, Ulf T. and Khong, Sei Zhen LU (2013) In SIAM Journal on Control and Optimization 51(1). p.353-379
Abstract
Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf 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 input-output 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 continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf 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 input-output 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 state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier--Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Control and Optimization
volume
51
issue
1
pages
353 - 379
publisher
SIAM Publications
external identifiers
  • Scopus:84876109660
ISSN
1095-7138
language
English
LU publication?
no
id
3c9d0bf0-b851-471e-90e7-568b75a2f409 (old id 4246727)
date added to LUP
2014-02-14 12:41:42
date last changed
2017-01-01 08:18:19
@article{3c9d0bf0-b851-471e-90e7-568b75a2f409,
  abstract     = {Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf 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 input-output 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 state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier--Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains.},
  author       = {Cantoni, Michael and Jönsson, Ulf T. and Khong, Sei Zhen},
  issn         = {1095-7138},
  language     = {eng},
  number       = {1},
  pages        = {353--379},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Control and Optimization},
  title        = {Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems},
  volume       = {51},
  year         = {2013},
}