Averaging for switched DAEs. Issue 1 (December 2013)

• Record Type: Journal Article
• Authors: Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 13:Issue 1(2013)
• Page Start: 489
• Page End: 490
• Publication Date: 2013-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201310237
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>Switched differential‐algebraic equations (switched DAEs) <tex-math notation="tex"><![CDATA[$E_{\sigma(t)}\dot{x}(t) = A_{\sigma(t)}x(t)$]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg3z40cnxb" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non‐switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so‐called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>