Geodesic
Differential-algebraic equations with regular local matrix pencils
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 39-47

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In the projector based framework, any regular linear DAE features several continuous time-varying characteristic subspaces that are independent of construction technicalities, among them the so-called sum-subspaces. As it is well-known, the local matrix pencils of a higher-index time-varying linear DAE do not reflect the global structure of the DAE in general. We show that, on the given interval, the local matrix pencils of the DAE are regular and reflect the global DAE structure if several of these characteristic subspaces are time-invariant. We discuss practicable methods to check the time-invariance of these subspaces. The corresponding class of DAEs is related to the class of DAEs formerly introduced and discussed by Yuri E. Boyarintsev.
Keywords: time-varying DAEs; local matrix pencil; regularity. 
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     title = {Differential-algebraic equations with regular local matrix pencils},
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     publisher = {mathdoc},
     volume = {6},
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René Lamour; Roswitha März. Differential-algebraic equations with regular local matrix pencils. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 4, pp. 39-47. http://geodesic.mathdoc.fr/item/VYURU_2013_6_4_a3/