Generalized solutions to hybrid systems with delays

We propose a framework that allows to study hybrid systems with delays through generalized concepts of solutions. Such generalized solutions have proved to be suitable for the analysis and design of hybrid control systems. Extending these concepts to systems with delays is motivated by control applications where hybrid feedback control laws play an important role but delays are often inevitable. Our first step characterizes a suitable phase space that is equipped with a suitable notion of convergence. The space of hybrid memory arcs under graphical convergence is considered. Regularity conditions on the hybrid data are then formulated in terms of the graphical topology. The new formulation enables two basic results regarding existence and well-posedness of solutions being established.