Cluster points and stability

Abstract

The relationship is examined between the stability properties of the solution of the discrete time system where A(·): R ⁿ →R ⁿ is a continuous non-linear map, and the set of cluster points L(x*) of the sequence {x_i } _i=0 ^∞. We show that the sequence is bounded if and only if the set L(x*) is contained in a compact set. We review also the contributions of other authors in this area.