Title: Contraction Analysis of Nonlinear DAE Systems,
Abstract: This paper studies the contraction properties of nonlinear
differential-algebraic equation (DAE) systems. Specifically we develop scalable
techniques for constructing the attraction regions associated with a particular
stable equilibrium, by establishing the relation between the contraction rates
of the original systems and the corresponding virtual extended systems. We show
that for a contracting DAE system, the reduced system always contracts faster
than the extended ones; furthermore, there always exists an extension with
contraction rate arbitrarily close to that of the original system. The proposed
construction technique is illustrated with a power system example in the
context of transient stability assessment.