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Generalized Jensen inequalities with application to stability analysis of systems with distributed delays over infinite time-horizons
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0001-9940-5929
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 69, 222-231 p.Article in journal (Refereed) PublishedText
Abstract [en]

The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite delays. In this paper, we first present a generalized integral inequality and its double integral extension. It is shown how these inequalities can be applied to improve the stability result for linear continuous-time systems with gamma-distributed delays. Then, for the discrete-time counterpart we provide an extended Jensen summation inequality with infinite sequences, which leads to less conservative stability conditions for linear discrete-time systems with Poisson-distributed delays. The improvements obtained by the introduced generalized inequalities are demonstrated through examples.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 69, 222-231 p.
Keyword [en]
Gamma-distributed delays, Lyapunov method, New integral and summation inequalities, Poisson-distributed delays
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-186908DOI: 10.1016/j.automatica.2016.02.038ISI: 000377312800024ScopusID: 2-s2.0-84961827087OAI: diva2:930142

QC 20160523

Available from: 2016-05-23 Created: 2016-05-16 Last updated: 2016-07-05Bibliographically approved

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Johansson, Karl Henrik
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