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Convergence and Equivalence Results for the Jensen's Inequality-Application to Time-Delay and Sampled-Data Systems
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
2011 (engelsk)Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, nr 7, s. 1660-1665Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2011. Vol. 56, nr 7, s. 1660-1665
Emneord [en]
Conservatism, fragmentation, Gruss inequality, Jensen's inequality, sampled-data systems, time-delay systems
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-38964DOI: 10.1109/TAC.2011.2121410ISI: 000293442300014Scopus ID: 2-s2.0-79960143376OAI: oai:DiVA.org:kth-38964DiVA, id: diva2:438817
Tilgjengelig fra: 2011-09-05 Laget: 2011-09-05 Sist oppdatert: 2017-12-08bibliografisk kontrollert

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