V. Acary, O. Bonnefon, and B. Brogliato, Nonsmooth modeling and simulation for switched circuits, vol.69, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00522358

V. Acary, H. De-jong, and B. Brogliato, Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems, Physica D: Nonlinear Phenomena, vol.269, pp.103-119, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00924044

V. Acary and F. Pérignon, Siconos: A software platform for modeling, simulation, analysis and control of nonsmooth dynamical systems, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00522740

M. Aizerman and E. Pyatnitskiy, Fundamentals of the theory of discontinuous systems. i. Avtom. Telemekh, 7 & 8, pp.33-48, 1974.

P. I. Barton, K. A. Khan, P. Stechlinski, and H. A. Watson, Computationally relevant generalized derivatives: theory, evaluation and applications, Optimization Methods and Software, vol.33, pp.1030-1072, 2018.

A. Benveniste, B. Caillaud, H. Elmqvist, K. Ghorbal, M. Otter et al., Structural analysis of multi-mode dae systems, Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control, pp.253-263, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01521918

K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, vol.14, 1996.

K. Camlibel, L. Iannelli, A. Tanwani, and S. Trenn, Differential-algebraic inclusions with maximal monotone operators, 2016 IEEE 55th Conference on Decision and Control (CDC), pp.610-615, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01366071

F. Facchinei and J. S. Pang, Finite-dimensional Variational Inequalities and Complementarity Problems, 2007.

A. F. Filippov, Differential equations with discontinuous right-hand side. Matematicheskii sbornik, vol.93, pp.99-128, 1960.

P. Hamann and V. Mehrmann, Numerical solution of hybrid systems of differential-algebraic equations, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.693-705, 2008.

E. Henningsson, H. Olsson, and L. Vanfretti, Dae solvers for large-scale hybrid models, Proceedings of the 13th International Modelica Conference, Regensburg, vol.157, 2019.

K. A. Khan, Branch-locking ad techniques for nonsmooth composite functions and nonsmooth implicit functions, Optimization Methods and Software, vol.33, issue.4-6, pp.1127-1155, 2018.

I. V. Matrosov, Existence of solutions of the algebro-differential equations. Automation and Remote Control, vol.67, pp.1408-1415, 2006.

I. V. Matrosov, On right-hand uniqueness of solutions to nondegenerated algebro-differential equations with discontinuances. Automation and Remote Control, vol.68, pp.9-17, 2007.

V. Mehrmann and L. Wunderlich, Hybrid systems of differential-algebraic equations-analysis and numerical solution, Journal of Process Control, vol.19, issue.8, pp.1218-1228, 2009.

J. S. Pang and D. E. Stewart, Differential variational inequalities, Mathematical Programming, vol.113, issue.2, pp.345-424, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01366027

A. Rocca, V. Acary, and B. Brogliato, Index-2 hybrid dae: a case study with well-posedness and numerical analysis, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02381489

R. T. Rockafellar and R. J. Wets, Variational Analysis, vol.317, 2009.

P. Stechlinski, M. Patrascu, and P. I. Barton, Nonsmooth differential-algebraic equations in chemical engineering, Computers & Chemical Engineering, vol.114, pp.52-68, 2018.

S. Trenn, Switched differential algebraic equations, Dynamics and Control of Switched Electronic Systems, pp.189-216, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01481155