On transverse exponential stability and its use in incremental stability, observer and synchronization (long version)

Vincent Andrieu (1) , Bayu Jayawardhana (2) , Laurent Praly (3)

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 Discrete Technology and Production Automation
3 CAS - Centre Automatique et Systèmes

We study the relation between the exponential stability of an invariant manifold and the existence of a Riemannian metric for which the flow is ''transversally'' contracting. More precisely, we investigate how the following properties are related to each other: i). A manifold is ''transversally'' exponentially stable; ii). The ''transverse'' linearization along any solution in the manifold is exponentially stable; iii). There exists a Riemannian metric for which the flow is ''transversally'' contracting. We show the relevance of these results in the study of incremental stability, observer design and synchronization.

Domaines: Automatique / Robotique

Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. On transverse exponential stability and its use in incremental stability, observer and synchronization (long version). 2013. ⟨hal-00860010v2⟩