In this paper we understand by a `hybrid system' one that combines features of continuous dynamical systems with characteristics of finite automata. We study a special class of such systems which we call the complementary-slackness class. We study existence and uniqueness of solutions in the special cases of linear and Hamiltonian complementary-slackness systems. For the latter class we also prove an energy inequality.

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions (msc 34A12), Implicit equations, differential-algebraic equations (msc 34A09), Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems (msc 37Jxx), Infinite-dimensional Hamiltonian systems (msc 37Kxx), Symplectic geometry, contact geometry (msc 53Dxx), Hamiltonian and Lagrangian mechanics (msc 70Hxx), Simulation (msc 68U20), Variable structure systems (msc 93B12)
Department of Operations Research, Statistics, and System Theory [BS]

van der Schaft, A.J, & Schumacher, J.M. (1995). The complementary-slackness class of hybrid systems. Department of Operations Research, Statistics, and System Theory [BS]. CWI.