K. M. Anstreicher, Generation of feasible descent directions in continuous time linear programming, 1983.

A. V. Arutyunov and S. M. Aseev, State constraints in optimal control. The degeneracy phenomenon, Systems & Control Letters, vol.26, issue.4, pp.267-273, 1995.
DOI : 10.1016/0167-6911(95)00021-Z

P. Ballard, The Dynamics of Discrete Mechanical Systems with Perfect Unilateral Constraints, Archive for Rational Mechanics and Analysis, vol.154, issue.3, pp.199-274, 2000.
DOI : 10.1007/s002050000105
URL : https://hal.archives-ouvertes.fr/hal-00111308

H. Benabdellah, C. Castaing, A. Salvadori, and A. Syam, Nonconvex Sweeping Process, Journal of Applied Analysis, vol.2, issue.2, pp.217-240, 1996.
DOI : 10.1515/JAA.1996.217

A. Berman, Plemmons: Nonnegative Matrices in The Mathematical Sciences, Computer Science and Applied Mathematics. Academic, 1979.

H. Brezis, Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert, 1973.

B. Brogliato, Nonsmooth Mechanics, 1999.
DOI : 10.1007/978-1-4471-0557-2
URL : https://hal.archives-ouvertes.fr/hal-01236953

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

B. Brogliato, Absolute stability and the Lagrange???Dirichlet theorem with monotone multivalued mappings, Systems & Control Letters, vol.51, issue.5, pp.343-353, 2004.
DOI : 10.1016/j.sysconle.2003.09.007
URL : https://hal.archives-ouvertes.fr/inria-00071792

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, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control. Theory and Applications, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01338369

B. Brogliato, S. Niculescu, and P. Orhant, On the control of finite-dimensional mechanical systems with unilateral constraints, IEEE Transactions on Automatic Control, vol.42, issue.2, pp.200-215, 1997.
DOI : 10.1109/9.554400

B. Brogliato, A. A. Ten-dam, L. Paoli, F. Genot, and M. Abadie, Numerical simulation of finite dimensional multibody nonsmooth mechanical systems, Applied Mechanics Reviews, vol.55, issue.2, pp.107-150, 2002.
DOI : 10.1115/1.1454112
URL : https://hal.archives-ouvertes.fr/hal-01349852

K. Camlibel, 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

K. Camlibel, 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

C. Castaing, D. Ha, T. X. Valadier, and M. , Evolution equations governed by the sweeping process . Set-Valued Anal, pp.109-139, 1993.
DOI : 10.1007/bf01027688

C. Castaing and M. D. Monteiro-marques, Evolution problems associated with nonconvex closed moving sets with bounded variation, Portugaliae Math, vol.1, pp.73-87, 1996.

D. Cobb, On the solutions of linear differential equations with singular coefficients, Journal of Differential Equations, vol.46, issue.3, pp.310-323, 1982.
DOI : 10.1016/0022-0396(82)90097-3

L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics. Boca Raton, 1992.

F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, vol I & II of Springer Series in Operations Research, 2003.

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

D. Goeleven, D. Motreanu, Y. Dumont, and M. Rochdi, Variational and Hemivariational Inequalities: Theory, Methods and Applications, vol. I: Unilateral Analysis and Unilateral Mechanics. Nonconvex Optimization and its Applications, Kluwer, vol.70, 2003.
DOI : 10.1007/978-1-4419-8758-7

R. F. Hartl, S. P. Sethi, and R. G. Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, vol.37, issue.2, pp.181-218, 1995.
DOI : 10.1137/1037043

W. P. Heemels, Linear Complementarity Systems. A Study in Hybrid Dynamics, 1999.
DOI : 10.1137/s0036139997325199
URL : https://hal.archives-ouvertes.fr/hal-00756195

W. P. Heemels and B. Brogliato, The Complementarity Class of Hybrid Dynamical Systems, European Journal of Control, vol.9, issue.2-3, pp.311-349, 2003.
DOI : 10.3166/ejc.9.322-360

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-00756195

J. I. Imura, Well-posedness analysis of switch-driven piecewise affine systems, IEEE Transactions on Automatic Control, vol.48, issue.11, pp.1926-1935, 2003.
DOI : 10.1109/TAC.2003.819075

M. Jean, The non-smooth contact dynamics method, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.235-257, 1999.
DOI : 10.1016/S0045-7825(98)00383-1
URL : https://hal.archives-ouvertes.fr/hal-01390459

A. Juloski, W. P. Heemels, and B. Brogliato, Observer design for Lur'e systems with multivalued mappings, IFAC World Congress Prague, pp.4-8, 2005.

P. Krejci and A. Vladimorov, Polyhedral sweeping processes with oblique reflection in the space of regulated functions, Set-Valued Analysis, vol.11, issue.1, pp.91-110, 2003.
DOI : 10.1023/A:1021980201718

M. Kunze, M. Marques, and M. D. , Existence of solutions for degenerate sweeping processes, J. Convex Anal, vol.4, pp.165-176, 1997.

M. Kunze, M. Marques, and M. D. , On parabolic quasi-variational inequalities and state-dependent sweeping processes, Topological Methods in Nonlinear Analysis, vol.12, issue.1, pp.179-191, 1998.
DOI : 10.12775/TMNA.1998.036
URL : http://www-users.mat.umk.pl/~tmna/files/v12n1-12.pdf

M. Kunze, M. Marques, and M. D. , An introduction to Moreau's sweeping process Impact in Mechanical systems: Analysis and Modelling, Lecture Notes in Physics, vol.551, pp.1-60, 2000.

M. Kunze, M. Marqufs, and M. D. , Yosida???Moreau Regularization of Sweeping Processes with Unbounded Variation, Journal of Differential Equations, vol.130, issue.2, pp.292-306, 1996.
DOI : 10.1006/jdeq.1996.0144

W. Q. Liu, W. Y. Lan, and K. L. Teo, On initial instantaneous jumps of singular systems, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1650-1655, 1995.
DOI : 10.1109/9.412639

Y. J. Lootsma, A. J. Van-der-schaft, and K. Camlibel, Uniqueness of solutions of linear relay systems, Automatica, vol.35, issue.3, pp.467-478, 1999.
DOI : 10.1016/S0005-1098(98)90177-7

P. Lotstedt, Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints, SIAM Journal on Applied Mathematics, vol.42, issue.2, pp.281-296, 1982.
DOI : 10.1137/0142022
URL : https://hal.archives-ouvertes.fr/hal-01399632

M. Mabrouk, A unified variational model for the dynamics of perfect unilateral constraints, European Journal of Mechanics - A/Solids, vol.17, issue.5, pp.819-842, 1998.
DOI : 10.1016/S0997-7538(98)80007-7

P. Machanda and A. H. Siddiqi, Rate dependent evolution quasivariational inequalities and statedependent sweeping processes, Adv. in Nonlinear Var. Inequal, vol.5, issue.1, pp.1-16, 2002.

M. Marques and M. P. , Differential Inclusions in NonSmooth Mechanical Problems: Shocks and Dry Friction, Birkhauser, 1993.
DOI : 10.1007/978-3-0348-7614-8

J. J. Moreau, Les liaisons unilatérales et le principe de Gauss, Comptes Rendus de l' des Sci, vol.256, pp.871-874, 1963.

J. J. Moreau, Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints, SIAM Journal on Control, vol.4, issue.1, pp.153-158, 1966.
DOI : 10.1137/0304014
URL : https://hal.archives-ouvertes.fr/hal-01379713

J. J. Moreau, Rafle par un convexe variable (première partie), exposé no 15. Séminaire d'analyse convexe, p.43, 1971.

J. J. Moreau, Rafle par un convexe variable (deuxième partie) exposé no 3. Séminaire d'analyse convexe, p.36, 1972.

J. J. Moreau, Problme d'évolution associ´cassoci´c a un convexe mobile d'un espace hilbertien. Comptes Rendus de l'AcadTmie des Sci, Séries A-B, t, pp.791-794, 1973.
DOI : 10.24033/bsmf.1625

J. J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, Journal of Differential Equations, vol.26, issue.3, pp.347-374, 1977.
DOI : 10.1016/0022-0396(77)90085-7

J. J. Moreau, Approximation en graphe d'une évolution discontinue. RAIRO Analyse numérique/ Numer, Anal, vol.12, pp.75-84, 1978.
DOI : 10.1051/m2an/1978120100751

J. J. Moreau, Liaisons unilatérales sans frottement et chocs inélastiques Comptes Rendus de l'AcadTmie des Sci. 296 serie II, pp.1473-1476, 1983.

J. J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, Nonsmooth Mechanics and Applications CISM, Courses and Lectures, pp.1-82, 1988.
DOI : 10.1007/978-3-7091-2624-0_1

J. J. Moreau, Some numerical methods in multibody dynamics: Application to granular materials, Eur. J. Mech. A/Solids supp, issue.4, pp.93-114, 1994.

J. J. Moreau, Numerical aspects of the sweeping process, Computer Methods in Applied Mechanics and Engineering, vol.177, issue.3-4, pp.329-349, 1999.
DOI : 10.1016/S0045-7825(98)00387-9
URL : https://hal.archives-ouvertes.fr/hal-01349847

J. J. Moreau, An introduction to Unilateral Dynamics, Novel Approaches in Civil Engineering, Series: Lecture Notes in Applied and Computational Mechanics, 2003.
DOI : 10.1007/978-3-540-45287-4_1

J. S. Pang and D. Stewart, Differential variational inequalities, Mathematical Programming, vol.12, issue.2, 2004.
DOI : 10.1007/s10107-004-0544-5
URL : https://hal.archives-ouvertes.fr/hal-01366027

A. Perold, Fundamentals of a continuous time simplex method, 1978.

A. Y. Pogromsky, W. P. Heemels, and H. Nijmeijer, On solution concepts and well-posedness of linear relay systems, Automatica, vol.39, issue.12, pp.2139-2147, 2003.
DOI : 10.1016/S0005-1098(03)00237-1

A. Saberi and P. Sannuti, Cheap and singular controls for linear quadratic regulators, IEEE Transactions on Automatic Control, vol.32, issue.3, pp.208-219, 1987.
DOI : 10.1109/TAC.1987.1104574

M. K. Sain and J. L. Massey, Invertibility of linear time-invariant dynamical systems, IEEE Transactions on Automatic Control, vol.14, issue.2, pp.141-149, 1969.
DOI : 10.1109/TAC.1969.1099133

P. Sannuti, Direct singular pertubation analysis of high gain and cheap control problem, Automatica, vol.19, issue.1, pp.424-440, 1983.

P. Sannuti and A. Saberi, Special coordinate basis for multivariable linear systems???finite and infinite zero structure, squaring down and decoupling, International Journal of Control, vol.45, issue.5, pp.1655-1704, 1987.
DOI : 10.1109/TAC.1981.1102551

P. Sannuti and H. Wason, Multiple time-scale decomposition in cheap control problems--Singular control, IEEE Transactions on Automatic Control, vol.30, issue.7, pp.633-644, 1985.
DOI : 10.1109/TAC.1985.1104031

M. Schatzman, Sur une classe de problémes hyperboliques non linéaires. Comptes Rendus de l'Académie des Sci Série A 277, pp.671-674, 1973.

M. Schatzman, A class of nonlinear differential equations of second order in time, Nonlinear Analysis: Theory, Methods & Applications, vol.2, issue.3, pp.355-373, 1978.
DOI : 10.1016/0362-546X(78)90022-6
URL : https://hal.archives-ouvertes.fr/hal-01294058

L. Schwartz, Analyse III, Calcul Intégral, Hermann, 1993.

A. H. Siddiqi and P. Machanda, Variants of Moreau's sweeping process, Adv. Nonlinear Var. Inequal, vol.5, issue.1, pp.17-28, 2002.

A. H. Siddiqi, P. Machanda, and M. Brokate, On Some Recent Developments Concerning Moreau???s Sweeping Process, International Conference on Emerging Areas in Industrial and applied mathematics. GNDU Amritsar, 2001.
DOI : 10.1007/978-1-4613-0263-6_15

D. Stewart, Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlev??'s Problem, Archive for Rational Mechanics and Analysis, vol.145, issue.3, pp.215-260, 1998.
DOI : 10.1007/s002050050129

D. A. Stewart, E. Dwarshuis, and J. C. Willems, Rigid body dynamics with friction and impact The contact problem for linear continuous-time dynamical systems: a geometric approach, SIAM Rev. IEEE Trans. Autom. Control, vol.42, issue.424, pp.3-39, 1997.

L. Thibault, Sweeping process with regular and nonregular sets, Journal of Differential Equations, vol.193, issue.1, pp.1-26, 2003.
DOI : 10.1016/S0022-0396(03)00129-3
URL : https://doi.org/10.1016/s0022-0396(03)00129-3

A. J. Van-der-schaft and J. M. Schumacher, An Introduction to Hybrid Dynamical Systems, 2000.
DOI : 10.1007/BFb0109998

A. J. Van-der-schaft and J. M. Schumacher, The complementary-slackness class of hybrid systems, Mathematics of Control, Signals and Systems, vol.11, issue.3, pp.266-301, 1996.
DOI : 10.1007/978-1-4757-2101-0

A. J. Van-der-schaft and J. M. Schumacher, Complementarity modeling of hybrid systems, IEEE Transactions on Automatic Control, vol.43, issue.4, pp.483-490, 1998.
DOI : 10.1109/9.664151