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Convergence and Equivalence Results for the Jensen's Inequality-Application to Time-Delay and Sampled-Data Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2011 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 7, 1660-1665 p.Article in journal (Refereed) Published
Abstract [en]

The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gruss Inequality. It has been reported in the literature that fragmentation (or partitioning) schemes allow to empirically improve the results. We prove here that the Jensen's gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large. Nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases. Finally, a family of bounds is characterized and a comparison with other bounds of the literature is provided. It is shown that the other bounds are equivalent to Jensen's and that they exhibit interesting well-posedness and linearity properties which can be exploited to obtain better numerical results.

Place, publisher, year, edition, pages
2011. Vol. 56, no 7, 1660-1665 p.
Keyword [en]
Conservatism, fragmentation, Gruss inequality, Jensen's inequality, sampled-data systems, time-delay systems
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-38964DOI: 10.1109/TAC.2011.2121410ISI: 000293442300014ScopusID: 2-s2.0-79960143376OAI: diva2:438817
Available from: 2011-09-05 Created: 2011-09-05 Last updated: 2011-09-05Bibliographically approved

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Briat, Corentin
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