The nature of solutions to linear passive complementarity systems

Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the 'complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of 'regular states' turns out to be invariant under the dynamics.