Transverse exponential stability and applications

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

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 ITM
3 CAS - Centre Automatique et Systèmes

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 field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique

Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. Transverse exponential stability and applications. IEEE Transactions on Automatic Control, 2016, 61 (11), pp.3396 - 3411. ⟨10.1109/TAC.2016.2528050⟩. ⟨hal-01232758⟩