Passivity and complementarity
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KünyeÇamlıbel, M.K., Lannelli, L., Vasca, F. (2014). Passivity and complementarity. Mathematical Programming, 145 (1-2), pp. 531-563. http://dx.doi.org/10.1007/s10107-013-0678-4.
This paper studies the interaction between the notions of passivity of systems theory and complementarity of mathematical programming in the context of complementarity systems. These systems consist of a dynamical system (given in the form of state space representation) and complementarity relations. We study existence, uniqueness, and nature of solutions for this system class under a passivity assumption on the dynamical part. A complete characterization of the initial states and the inputs for which a solution exists is given. These initial states are called consistent states. For the inconsistent states, we introduce a solution concept in the framework of distributions.