Higher-order spectral analysis and weak asymptotic stability of convex processes

This paper deals with the asymptotic stability analysis of a discrete dynamical inclusion whose right-hand side is a convex process.We provide necessary and sufficient conditions for weak asymptotic stability, and obtain sharp estimates for the asymptotic null-controllability set. These estimates involve not only standard, but also higher-order spectral information on the convex process and its adjoint. © 2005 Elsevier Inc. All rights reserved.