Stability of diced systems

Diced systems are defined as autonomous systems governed by ordinary differential equations having discontinuities (in Rn) on submanifolds where one or more of the state variables takes an integer value. Such systems may be regarded as approximations of continuous systems or as representative models of a class of discontinuous systems. Trajectories of such systems (for a given initial state) are readily calculated and may exhibit complex sliding-mode segments. Asymptotic properties of such trajectories are discussed and classified. Motivation is given in terms of observed properties of interconnected power systems.