# Contraction Analysis of Nonlinear DAE Systems

## TL;DR

This paper investigates the contraction properties of nonlinear DAE systems, providing scalable methods to determine attraction regions and analyze stability, with applications demonstrated in power system transient stability.

## Contribution

It introduces a novel scalable technique linking contraction rates of original and extended DAE systems, enhancing stability analysis methods.

## Key findings

- Contracting DAE systems have faster reduced systems.
- Existence of extensions with contraction rates close to original.
- Application to power system transient stability assessment.

## 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.