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Averaging for switched DAEs
Author(s) -
Iannelli Luigi,
Pedicini Carmen,
Trenn Stephan,
Vasca Francesco
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310237
Subject(s) - ode , ordinary differential equation , consistency (knowledge bases) , control theory (sociology) , differential algebraic equation , mathematics , limit (mathematics) , differential (mechanical device) , class (philosophy) , algebraic number , computer science , differential equation , topology (electrical circuits) , mathematical analysis , discrete mathematics , physics , combinatorics , control (management) , artificial intelligence , thermodynamics
Switched differential‐algebraic equations (switched DAEs) $E_{\sigma(t)}\dot{x}(t) = A_{\sigma(t)}x(t)$ 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 & Co. KGaA, Weinheim)