V. Acary, O. Bonnefon, and B. Brogliato, Time-Stepping Numerical Simulation of Switched Circuits Within the Nonsmooth Dynamical Systems Approach, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.29, issue.7, pp.1042-1055, 2010.
DOI : 10.1109/TCAD.2010.2049134

V. Acary, O. Bonnefon, and B. Brogliato, Nonsmooth Modeling and Simulation for Switched Circuits, Lecture Notes in Electrical Engineering, vol.69, 2011.
DOI : 10.1007/978-90-481-9681-4
URL : https://hal.archives-ouvertes.fr/inria-00522358

V. Acary, B. Brogliato, and D. Goeleven, Higher order Moreau???s sweeping process: mathematical formulation and numerical simulation, Mathematical Programming, vol.43, issue.4, pp.133-217, 2008.
DOI : 10.1007/BFb0109998
URL : http://www.inrialpes.fr/bipop/publis/AcBrGo2008MATHPROGA.pdf

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.
DOI : 10.1016/j.physd.2013.11.013
URL : https://hal.archives-ouvertes.fr/hal-00924044

J. Andersson and K. Leuven, A General-Purpose Software Framework for Dynamic Optimization, ESAT/SCD) and Optimization in Engineering Center, p.3001, 2013.

C. Batlle, E. Fossas, I. Merillas, and A. Miralles, Generalized discontinuous conduction modes in the complementarity formalism, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.52, issue.8, pp.52447-451, 2005.
DOI : 10.1109/TCSII.2005.849010

B. Brogliato, Some perspectives on the analysis and control of complementarity systems, IEEE Transactions on Automatic Control, vol.48, issue.6, pp.918-935, 2003.
DOI : 10.1109/TAC.2003.812777
URL : https://hal.archives-ouvertes.fr/hal-01660014

B. Brogliato, Some results on the controllability of planar variational inequalities, Systems & Control Letters, vol.54, issue.1, pp.65-71, 2005.
DOI : 10.1016/j.sysconle.2004.06.006
URL : https://hal.archives-ouvertes.fr/inria-00071798

B. Brogliato, A. Daniilidis, C. Lemaréchal, and V. Acary, On the equivalence between complementarity systems, projected systems and differential inclusions, Systems & Control Letters, vol.55, issue.1, pp.45-51, 2006.
DOI : 10.1016/j.sysconle.2005.04.015
URL : https://hal.archives-ouvertes.fr/inria-00071475

B. Brogliato and D. Goeleven, Well-posedness, stability and invariance results for a class of multivalued Lur???e dynamical systems, Nonlinear Analysis: Theory, Methods & Applications, vol.74, issue.1, pp.195-212, 2011.
DOI : 10.1016/j.na.2010.08.034
URL : https://hal.archives-ouvertes.fr/hal-01633239

B. Brogliato and D. Goeleven, Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur'e dynamical systems, Journal of Convex Analysis, vol.20, issue.3, pp.881-900, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00825601

B. Brogliato and L. Thibault, Existence and uniqueness of solutions for non-autonomous complementarity dynamical systems, Journal of Convex Analysis, vol.17, issue.3, pp.961-990, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00756226

T. H. Cao and B. S. Mordukhovich, Optimal control of a perturbed sweeping process via discrete approximations, Discrete and Continuous Dynamical Systems - Series B, vol.21, issue.10, pp.3331-3358, 2015.
DOI : 10.3934/dcdsb.2016100

M. K. Çamlibel, J. Pang, and J. Shen, Lyapunov Stability of Complementarity and Extended Systems, SIAM Journal on Optimization, vol.17, issue.4, pp.1056-1101, 2006.
DOI : 10.1137/050629185

M. K. Çamlibel, W. P. Heemels, and J. M. Schumacher, Consistency of a time-stepping method for a class of piecewise-linear networks, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.49, issue.3, pp.349-357, 2002.
DOI : 10.1109/81.989170

M. K. Çamlibel, W. P. Heemels, and J. M. Schumacher, On Linear Passive Complementarity Systems, European Journal of Control, vol.8, issue.3, pp.220-237, 2002.
DOI : 10.3166/ejc.8.220-237

M. K. Çamlibel and L. Iannelli, Passivity and complementarity, Mathematical Programming, vol.11, issue.4, pp.531-563, 2014.
DOI : 10.1002/rnc.592

L. Cesari, Optimization-Theory and Applications: Problems with Ordinary Differential Equations, 2012.
DOI : 10.1007/978-1-4613-8165-5

G. Colombo, R. Henrion, N. D. Hoang, and B. S. Mordukhovich, Optimal control of the sweeping process, Dyn. Contin. Discrete Impuls. Syst.-Ser. B, vol.19, pp.117-159, 2012.

G. Colombo, R. Henrion, D. H. Nguyen, and B. S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, Journal of Differential Equations, vol.260, issue.4, pp.3397-3447, 2016.
DOI : 10.1016/j.jde.2015.10.039

R. Cottle, J. Pang, and R. Stone, The linear complementarity problem, SIAM, 2009.

M. D. De-pinho, Mixed constrained control problems, Journal of Mathematical Analysis and Applications, vol.278, issue.2, pp.293-307, 2003.
DOI : 10.1016/S0022-247X(02)00351-7

F. Facchinei and J. Pang, Finite-dimensional variational inequalities and complementarity problems, 2007.

C. Georgescu, B. Brogliato, and V. Acary, Switching, relay and complementarity systems: A tutorial on their well-posedness and relationships, Physica D: Nonlinear Phenomena, vol.241, issue.22, pp.2411985-2002, 2012.
DOI : 10.1016/j.physd.2011.10.014
URL : https://hal.archives-ouvertes.fr/hal-00646982

D. Goeleven, Existence and Uniqueness for a Linear Mixed Variational Inequality Arising in Electrical Circuits with Transistors, Journal of Optimization Theory and Applications, vol.40, issue.3, pp.397-406, 2008.
DOI : 10.1017/S0334270000010912
URL : https://hal.archives-ouvertes.fr/hal-00919738

D. Goeleven and B. Brogliato, Stability and Instability Matrices for Linear Evolution Variational Inequalities, IEEE Transactions on Automatic Control, vol.49, issue.4, pp.521-534, 2004.
DOI : 10.1109/TAC.2004.825654
URL : http://www.inrialpes.fr/bipop/people/brogliato/IEEE-TAC.2004.pdf

L. Guo, G. Lin, and J. J. Ye, Solving Mathematical Programs with Equilibrium Constraints, Journal of Optimization Theory and Applications, vol.19, issue.1, pp.234-256, 2015.
DOI : 10.1080/1055678041001697659

L. Guo and J. J. Ye, Necessary Optimality Conditions for Optimal Control Problems with Equilibrium Constraints, SIAM Journal on Control and Optimization, vol.54, issue.5, pp.2710-2733, 2016.
DOI : 10.1137/15M1013493

L. Han, A. Tiwari, M. K. Çamlibel, and J. Pang, Convergence of Time-Stepping Schemes for Passive and Extended Linear Complementarity Systems, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3768-3796, 2009.
DOI : 10.1137/080725258

W. P. Heemels, M. K. Çamlibel, J. Schumacher, and B. Brogliato, Observer-based control of linear complementarity systems, International Journal of Robust and Nonlinear Control, vol.50, issue.5, pp.1193-1218, 2011.
DOI : 10.1016/0024-3795(83)90062-9
URL : https://hal.archives-ouvertes.fr/hal-00834580

W. P. Heemels, J. M. Schumacher, and S. Weiland, Linear Complementarity Systems, SIAM Journal on Applied Mathematics, vol.60, issue.4, pp.1234-1269, 2000.
DOI : 10.1137/S0036139997325199
URL : https://hal.archives-ouvertes.fr/hal-00834580

L. Iannelli, F. Vasca, and G. Angelone, Computation of Steady-State Oscillations in Power Converters Through Complementarity, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.58, issue.6, pp.1421-1432, 2011.
DOI : 10.1109/TCSI.2010.2094390

C. Kanzow and A. Schwartz, Mathematical Programs with Equilibrium Constraints: Enhanced Fritz John-conditions, New Constraint Qualifications, and Improved Exact Penalty Results, SIAM Journal on Optimization, vol.20, issue.5, pp.2730-2753, 2010.
DOI : 10.1137/090774975

C. Kanzow and A. Schwartz, A New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties, SIAM Journal on Optimization, vol.23, issue.2, pp.770-798, 2013.
DOI : 10.1137/100802487

D. Leenaerts, On linear dynamic complementary systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.46, issue.8, pp.1022-1026, 1999.
DOI : 10.1109/81.780383

S. Leyffer, G. López-calva, and J. Nocedal, Interior Methods for Mathematical Programs with Complementarity Constraints, SIAM Journal on Optimization, vol.17, issue.1, pp.52-77, 2006.
DOI : 10.1137/040621065
URL : http://www.ece.northwestern.edu/~nocedal/PDFfiles/mpec.pdf

Z. Luo, J. Pang, and D. Ralph, Mathematical Programs with Equilibrium Constraints, 1996.
DOI : 10.1017/CBO9780511983658

J. Pang and D. E. Stewart, Solution dependence on initial conditions in differential variational inequalities, Mathematical Programming, vol.81, issue.1-2, pp.429-460, 2009.
DOI : 10.1007/978-3-642-02431-3

B. Passenberg, P. E. Caines, M. Leibold, O. Stursberg, and M. Buss, Optimal Control for Hybrid Systems With Partitioned State Space, IEEE Transactions on Automatic Control, vol.58, issue.8, pp.582131-2136, 2013.
DOI : 10.1109/TAC.2013.2246112

H. Scheel and S. Scholtes, Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity, Mathematics of Operations Research, vol.25, issue.1, pp.1-22, 2000.
DOI : 10.1287/moor.25.1.1.15213

V. Sessa, L. Iannelli, and F. Vasca, A Complementarity Model for Closed-Loop Power Converters, IEEE Transactions on Power Electronics, vol.29, issue.12, pp.6821-6835, 2014.
DOI : 10.1109/TPEL.2014.2306975

V. Sessa, L. Iannelli, F. Vasca, and V. Acary, A complementarity approach for the computation of periodic oscillations in piecewise linear systems, Nonlinear Dynamics, vol.269, issue.5, pp.1255-1273, 2016.
DOI : 10.1016/j.physd.2013.11.013

M. S. Shaikh and P. E. Caines, On the Hybrid Optimal Control Problem: Theory and Algorithms, IEEE Transactions on Automatic Control, vol.52, issue.9, pp.1587-1603, 2007.
DOI : 10.1109/TAC.2007.904451

J. Shen, Robust Non-Zenoness of Piecewise Affine Systems with Applications to Linear Complementarity Systems, SIAM Journal on Optimization, vol.24, issue.4, pp.2023-2056, 2014.
DOI : 10.1137/130937068

J. Shen and J. Pang, Linear Complementarity Systems: Zeno States, SIAM Journal on Control and Optimization, vol.44, issue.3, pp.1040-1066, 2005.
DOI : 10.1137/040612270
URL : http://www.math.umbc.edu/~shenj/research/sicon_61227.pdf

H. J. Sussmann, A maximum principle for hybrid optimal control problems, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), pp.425-430, 1999.
DOI : 10.1109/CDC.1999.832814

A. Tanwani, B. Brogliato, and C. Prieur, Stability and observer design for Lur'e systems with multivalued, non-monotone, time-varying nonlinearities and state jumps, SIAM Journal on Control and Optimization, vol.56, issue.2, pp.3639-3672, 2014.

A. Tanwani, B. Brogliato, and C. Prieur, Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities, SIAM Journal on Control and Optimization, vol.56, issue.2, 2018.
DOI : 10.1137/16M1083657
URL : https://hal.archives-ouvertes.fr/hal-01360325

E. Trélat, Optimal Control and Applications to Aerospace: Some Results and Challenges, Journal of Optimization Theory and Applications, vol.21, issue.1, pp.713-758, 2012.
DOI : 10.1016/0005-1098(85)90107-4

F. Vasca, L. Iannelli, M. K. Çamlibel, and R. Frasca, A New Perspective for Modeling Power Electronics Converters: Complementarity Framework, IEEE Transactions on Power Electronics, vol.24, issue.2, pp.456-468, 2009.
DOI : 10.1109/TPEL.2008.2007420

J. J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints, Journal of Mathematical Analysis and Applications, vol.307, issue.1, pp.350-369, 2005.
DOI : 10.1016/j.jmaa.2004.10.032
URL : https://doi.org/10.1016/j.jmaa.2004.10.032