On robustness in the gap metric and coprime factor uncertainty for LTV systems

In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems...

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Bibliographic Details
Published inSystems & control letters Vol. 80; pp. 16 - 22
Main Author Djouadi, Seddik M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2015
Subjects
Coprime factorization
Gap metric
Robust stabilization
Time-varying
Coprime factorization
Robust stabilization
Time-varying
Gap metric
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Summary:In this paper, we study the problem of robust stabilization for discrete linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2015.03.006