Well-posedness of linear complementarity systems

In hybrid systems theory one often assumes (i) existence of solutions (ii) uniqueness of solutions and (iii) non-Zenoness (i.e. at most a finite number of events in a finite time interval). Sufficient conditions for these properties are rarely given. We present the state-of-the-art of the well-posedness results for the linear complementarity class of hybrid systems. Results on global existence of solutions and exclusion of accumulations of event times are given. Moreover, we present several examples of hybrid systems showing the interaction between the solution concept, non-Zeno assumptions and well-posedness.