Systems depending on a small parameter " are considered. Suucient conditions are stated, including a convergence property for trajectories, a homogeneity property and a periodicity property, such that global uniform-exponential stability for the system corresponding to " = 0 implies global uniform-exponential stability for the systems corresponding to " > 0 suuciently small. Examples illustrate...

Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signi cant importance. It is especially so when attempting to bridge the gap between theory and practice. This paper addresses the question of the applicability of contraction theory to the des...

In this article, we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to uncertainties. We first extend the well-known Datko lemma framework of considered class systems. Thanks generalization, provide characterizations uniform (with respect uncertainties) local, semi-global, and global exponential stability, through existence coercive non-coercive Lya...