A complete stability analysis of planar linear systems under saturation

A complete stability analysis is performed on a planar system of the form x/spl dot/=/spl sigma/(Ax), where A is a Hurwitz matrix and /spl sigma/ is the saturation function. Necessary and sufficient conditions for the system to be globally asymptotically stable or to have a closed trajectory are explicitly given in terms of the entries of A. These conditions also indicate that the system always has a closed trajectory if it is not globally asymptotically stable.