Linear complementarity systems

We introduce a new class of dynamical systems called linear complementarity systems. The time evolution of these systems consists of a series of conti nuous phases separated by events which cause a change in dynamics and possi bly a jump in the state vector. The occurrence of events is governed by cer tain 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 inequalitie s playa role; for instance, in mechanics, electrical networks, piecewise li near systems, and dynamic optimization. We present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions.