Hybrid connections and time-scales in non-linear systems

Abstract

Hidden time-scales arising in hybrid-connected systems are studied by a manifold-based approach. This geometric interpretation of time-scales permits the use of equilibrium and conservation properties to characterize a transformation leading the model to a well-posed form, for which an extensive literature is surveyed. As an illustration we apply a recent stability result. An analytical example is also included to show how to construct aggregate and equilibrium models.