Complementarity methods in the analysis of piecewise linear dynamical systems

The main object of this thesis is a class of piecewise linear dynamical systems that are related both to system theory and to mathematical programming. The dynamical systems in this class are known as complementarity systems. With regard to these nonlinear and nonsmooth dynamical systems, the research in the thesis concentrates on two themes: well-posedness and approximations. The well-posedness issue, in the sense of existence and uniqueness of solutions, is of considerable importance from a model validation point of view. In the thesis, sufficient conditions are established for the well-posedness of complementarity systems. Furthermore, an investigation is made of the convergence of approximations of these systems with an eye towards simulation.