Dissipative Systems and Complementarity Conditions

In this paper existence and uniqueness of solutions to linear complementarity systems (LCS) are considered. Complementarity systems are systems that are composed of differential equations, inequalities and switching logic. These systems can therefore be seen as a subclass of hybrid dynamical systems. The main result of this paper states that dissipativity of the underlying state space description of a LCS is a sufficient condition for existence of so-called initial solutions and guarantees uniqueness of the state trajectory. Applications of the results includeelectrical networks with diodes.