T. E. Stern, Piecewise-linear network theory, 1956.

M. K. Camlibel, W. P. Heemels, A. J. Van-der-schaft, and J. M. Schumacher, Switched networks and complementarity, IEEE Trans. Circuits Syst. I Reg. Pap, vol.50, issue.8, pp.1036-1046, 2003.

V. Acary, O. Bonnefon, and B. Brogliato, Time-stepping numerical simulation of switched circuits within the nonsmooth dynamical systems approach, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst, vol.29, issue.7, pp.1042-1055, 2010.

V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

J. Melin, A. Hultgren, and T. Lindstrom, Two types of limit cycles of a resonant converter modelled by threedimensional system, Nonlinear Anal. Hybrid Syst, vol.2, issue.4, pp.1275-1286, 2008.

X. Yang and G. Chen, Limit cycle and chaotic invariant sets in autonomous hybrid planar systems, Nonlinear Anal. Hybrid Syst, vol.2, issue.3, pp.952-957, 2008.

T. Aprille and T. Trick, A computer algorithm to determine the steady-state response of nonlinear oscillators, IEEE Trans. Circuit Theory, vol.19, issue.4, pp.354-360, 1972.

D. Flieller, P. Riedinger, and J. P. Louis, Computation and stability of limit cycles in hybrid systems, Nonlinear Anal. Theory Methods Appl, vol.64, issue.2, pp.352-367, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00119807

D. Li and J. Xu, A new method to determine the periodic orbit of a nonlinear dynamic systems and its period, Eng. Comput, vol.20, issue.4, pp.316-322, 2005.

R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems, 2004.

C. Theodosiou, A. Pournaras, and S. Natsiavas, On periodic steady state response and stability of Filippov-type mechanical models, Nonlinear Dyn, vol.66, issue.3, pp.355-376, 2011.

F. Bizzarri, A. Brambilla, and G. S. Gajani, Steady state computation and noise analysis of analog mixed signal circuits, IEEE Trans. Circuits Syst. I Reg. Pap, vol.59, issue.3, pp.541-554, 2012.

R. I. Leine, D. H. Van-campen, and A. De-kraker, Stick-slip vibrations induced by alternate friction models, Nonlinear Dyn, vol.16, issue.1, pp.41-54, 1998.

B. L. Van-de-vrande, D. H. Van-campen, and A. De-kraker, An approximate analysis of dry-friction-induced stick-slip vibrations by smoothing procedure, Nonlinear Dyn, vol.19, issue.2, pp.157-169, 1999.

P. Thota and H. Dankowicz, TC-HAT (T C): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems, SIAM J. Appl. Dyn. Syst, vol.7, issue.4, pp.1283-1322, 2008.

C. Lu and Y. Lin, A modified incremental harmonic balance method for rotary periodic motions, Nonlinear Dyn, vol.66, issue.4, pp.781-788, 2011.

M. Bonnin, M. Gilli, and P. P. Civalleri, A mixed timefrequency-domain approach for the analysis of a hysteretic oscillator, IEEE Trans. Circuits Syst. II Exp. Br, vol.52, issue.9, pp.525-529, 2005.

A. Brambilla, G. Gruosso, and G. Storti-gajani, MTFS mixed time-frequency method for the steady-state analysis of almost-periodic nonlinear circuits, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst, vol.31, issue.9, pp.1346-1355, 2012.

F. B. Duarte and J. Machado, Fractional describing function of systems with Coulomb friction, Nonlinear Dyn, vol.56, issue.4, pp.381-387, 2009.

Y. Huang and Y. Wang, Steady-state analysis for a class of sliding mode controlled systems using describing function method, Nonlinear Dyn, vol.30, issue.3, pp.223-241, 2002.

S. Engelberg, Limitations of the describing function for limit cycle prediction, IEEE Trans. Autom. Control, vol.47, issue.11, pp.1887-1890, 2002.

F. Vasca, L. Iannelli, and M. K. Camlibel, A new perspective for modeling power electronics converters: complementarity framework, IEEE Trans. Power Electron, vol.24, issue.2, pp.456-468, 2009.

J. M. Schumacher, Complementarity systems in optimization, Math. Program, vol.101, issue.1, pp.263-296, 2004.

V. Sessa, L. Iannelli, and F. Vasca, A complementarity model for closed-loop power converters, IEEE Trans. Power Electron, vol.29, issue.12, pp.6821-6835, 2014.

A. J. Van-der-schaft and J. M. Schumacher, Complementarity modeling of hybrid systems, IEEE Trans. Autom. Control, vol.43, pp.483-490, 1998.

W. P. Heemels, B. De-schutter, and A. Bemporad, Equivalence of hybrid dynamical model, Automatica, vol.37, issue.7, pp.1085-1091, 2001.

L. Iannelli and F. Vasca, Computation of limit cycles and forced oscillations in discrete-time piecewise linear feedback systems through a complementarity approach, 47th IEEE Conference on Decision and Control, pp.1169-1174, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01309168

L. Iannelli, F. Vasca, and V. Sessa, Computation of limit cycles in Lur'e systems, pp.1402-1407, 2011.

V. Sessa, L. Iannelli, and F. Vasca, Mixed linear complementarity problems for the analysis of limit cycles in piecewise linear systems, The 51st IEEE Conference on Decision and Control, pp.1023-1028, 2012.

V. Sessa, L. Iannelli, V. Acary, B. Brogliato, and F. Vasca, Computing period and shape of oscillations in piecewise linear Lur'e systems: a complementarity approach, The 52nd IEEE Conference on Decision and Control, pp.4680-4685, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00870282

F. Facchinei and J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Operations Research, 2003.

S. P. Dirkse and M. C. Ferris, The PATH solver: a nonmonotone stabilization scheme for mixed complementarity problems, Optim. Methods Softw, vol.5, pp.123-156, 1995.

R. Cottle, J. Pang, and R. Stone, The Linear Complementarity Problem, 2009.

M. S. Gowda and J. Pang, Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory, Math. Oper. Res, vol.19, issue.4, pp.831-879, 1994.

M. Farkas, Periodic Motions. Series in Applied Mathematical, 1994.

E. J. Doedel, AUTO: a program for the automatic bifurcation analysis of autonomous systems, Congr. Numer, vol.30, pp.1265-1284, 1981.

A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods, 1995.

R. U. Seydel, Practical Bifurcation and Stability Analysis, 1988.

V. Acary, Dynamics and Control of Switched Electroinic Systems, Advances in Industrial Control, 2012.

L. Han, A. Tiwari, M. K. Camlibel, and J. Pang, Convergence of time-stepping for passive and extended linear complementarity systems, SIAM J. Numer. Anal, vol.47, issue.5, pp.3768-3796, 2009.

J. Pang and D. E. Stewart, Differential variational inequalities, Math. Program, vol.113, pp.345-424, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01366027

K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptation, Biol. Cybern, vol.52, p.367376, 1985.

J. M. Goncalves, Region of stability for limit cycles in piecewise linear systems, IEEE Trans. Autom. Control, vol.50, issue.11, pp.1877-1882, 2005.

T. Hu, T. Thibodeau, and T. R. Teel, A unified Lyapunov approach to analysis of oscillations and stability for systems with piecewise linear elements, IEEE Trans. Autom. Control, vol.55, issue.12, pp.2864-2869, 2010.

H. K. Khalil, Nonlinear Systems, 2002.

W. P. Heemels, M. K. Camlibel, and J. M. Schumacher, A time-stepping method for relay systems, 39th IEEE Conference on Decision and Control, pp.4461-4466, 2000.

K. J. Astrom and C. Canudas-de-wit, Revisiting the LuGre friction model, IEEE Control Syst. Mag, vol.28, issue.6, pp.101-114, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00394988

A. Tonnelier, Cyclic negative feedback systems: what is the chance of oscillation?, Bull. Math. Biol, vol.76, issue.5, pp.1155-1193, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00919629

V. Acary, H. De-jong, and B. Brogliato, Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems. Phys. D Nonlinear Phenom, vol.269, pp.103-119, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00766266

M. Bernardo, C. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems, vol.163, 2008.