A switching system is a multimodal system with switching rules of a specific form. While the individual modes are given by (ordinary or partial) differential equations, the evolutionary behavior of a switching system involves some qualitatively new considerations. Such systems arise both as 'reduced order models' in the modeling of thermostats and other threshold-controlled systems involving nonlinear 'fast dynamics' (singular perturbation) and also in the implementation of feedback switching controls for multimodal systems. Investigation of switching systems and switching system models is proposed in three areas: obehavior of (classes of) switching systems as 'dynamical systems', i.e., stability, existence and characterization of periodic solutions, etc.; ogenericity and stability of behavior with respect to perturbation of parameters, especially near certain degeneracies; orelation to the world: 'engineering' applications and a deeper understanding of the relation of these switching system models to alternative (e.g., more detailed) models. The proposed research is foundational for the understanding of a wide class of applications involving interactions of continuous with discrete-event systems.
