The Flow of a DAE near a Singular Equilibrium

Authors:
R. E. Beardmore;R. Laister
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2002

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Abstract

We extend the differential-algebraic equation (DAE) taxonomy by assuming that the linearization of a DAE about a singular equilibrium has a particular index-2 Kronecker normal form. A Lyapunov--Schmidt procedure is used to reduce the DAE to a quasilinear normal form which is shown to posses quasi-invariant manifolds which intersect the singularity. In turn, this provides solutions of the DAE which pass through the singularity.