A notion of equivalence for linear complementarity problems with application to the design of non-smooth bifurcations

Abstract: Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to analyze, classify, and design non-smooth bifurcations in linear complementarity problems and their interconnection.