A Trajectory-Space Approach to Hybrid Systems

We develop a framework for studying dynamical properties of hybrid systems based on considering the space of all possible trajectories of the system. In this way it is possible to treat both nondeterministic systems and systems for which the evolution does not depend continuously on the initial conditions. We show that the trajectory space is compact for the class of upper-semicontinuous hybrid systems, obtain results on Zeno properties and invariant measures for systems with compact trajectory set. Since many classes of hybrid system can be recast in upper-semicontinuous form, these results are of general applicability.