Complete description of dynamics in the linear complementary-slackness class of hybrid systems

We introduce the class of linear complementary-slackness systems. The time 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 motivated by physical models in which both differential equations and inequalities play a role. We present a precise definition of linear complementary-slackness systems and give sufficient conditions for existence and uniqueness of solutions. The theory is illustrated by mechanical systems