On dynamics, complementarity and passivity: electrical networks with ideal diodes

In this paper we study linear passive electrical circuits mixed with ideal diodes and voltage/current sources within the framework of linear complementarity systems. Linear complementarity systems form a subclass of hybrid dynamical systems and as such questions about existence and uniqueness of solution trajectories are non-trivial and will be investigated here. The nature of the behaviour is analyzed and characterizations of the inconsistent states of the network are presented. Also explicit jump rules from these inconsistent states are given in various forms. Finally, these results lead to a generalization of the notion of passivity to linear complementarity systems.