A. Bemporad, M.K. Çamlibel, W.P.M.H. Heemels, A.J. van der Schaft, J.M. Schumacher, and B. De Schutter, "Further switched systems," Chapter 5 in Handbook of Hybrid Systems Control - Theory, Tools, Applications (J. Lunze and F. Lamnabhi-Lagarrigue, eds.), Cambridge, UK: Cambridge University Press, ISBN 978-0-521-76505-3, pp. 139-192, 2009.
Mixed logical dynamical systems and linear complementarity systems are representations of switched systems, which under the conditions described here are equivalent to piecewise affine systems. They are particularly useful for model-predictive control. The equivalences of several hybrid system models show that different models, which are suitable for specific analysis and design problems and have been investigated in detail, cover the same class of hybrid systems. The analysis of the well-posedness of the models leads to conditions on the model equations under which a unique solution exists.