The flow of a DAE near a singular equilibrium

Beardmore, R. E.; Laister, Robert

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.

• Journal Article Type: Article
• Publication Date: Jan 1, 2003
• Journal: SIAM Journal on Matrix Analysis and Applications
• Print ISSN: 0895-4798
• Electronic ISSN: 1095-7162
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 1
• Pages: 106-120
• DOI: https://doi.org/10.1137/S0895479800378660
• Keywords: differential algebraic equations, invariant manifold, singular equilibrium, matrix pencil
• Public URL: https://uwe-repository.worktribe.com/output/1037620
• Publisher URL: http://dx.doi.org/10.1137/S0895479800378660