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Robust Stability Analysis For Feedback Interconnections Of Time-Varying Linear Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2013 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 51, no 1, 353-379 p.Article in journal (Refereed) Published
Abstract [en]

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 L-2-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 L-2 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.

Place, publisher, year, edition, pages
2013. Vol. 51, no 1, 353-379 p.
Keyword [en]
feedback stability, Fredholm index, Hankel operators, integral quadratic constraints, nu-gap metric, time-varying systems, Toeplitz-Wiener-Hopf operators
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-120362DOI: 10.1137/100814676ISI: 000315578000015ScopusID: 2-s2.0-84876109660OAI: diva2:614558

QC 20130405

Available from: 2013-04-05 Created: 2013-04-04 Last updated: 2013-04-05Bibliographically approved

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Jönsson, Ulf T.
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