Linear Complementarity Systems

We introduce a new class of dynamical systems that we call "linear complementarity systems ". The evolution of these systems typically consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the Linear Complementarity Problem of mathematical programming. The framework we describe is suitable for certain situations in which both differential equations and inequalities play a role, for instance in mechanics, electrical networks, and dynamic optimization. We present a precise definition of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions. 1 Introduction In many technical and economic applications one encounters systems of differential equations and inequalities. For a quick roundup of examples, one may think of the following: motion of rigid bodies subject to unil...