Localizing Sets and Behavior of Trajectories of Time-Varying Systems

Abstract

For time-varying continuous-time dynamical systems (time-varying systems of differential equations), we establish a number of properties of the universal section and localizing set corresponding to a given localizing function. A classification is obtained for the behavior of trajectories of the system outside the localizing set. The results are an extension of those known for time-invariant continuous-time systems to the case of time-varying systems.