M. Konecny, W. Taha, J. Duracz, A. Duracz, and A. Ames, Enclosing the behavior of a hybrid system up to and beyond a Zeno point, 2013 IEEE 1st International Conference on Cyber-Physical Systems, Networks, and Applications (CPSNA), pp.120-125, 2013.
DOI : 10.1109/CPSNA.2013.6614258

W. Taha and A. Duracz, Acumen: An Open-Source Testbed for Cyber-Physical Systems Research, pp.118-130
DOI : 10.1007/978-3-540-71070-7_15
URL : https://hal.archives-ouvertes.fr/hal-01490406

R. E. Moore, Methods and applications of interval analysis, SIAM, 1979.
DOI : 10.1137/1.9781611970906

M. Berz, Computational differentiation: techniques, applications , and tools, 1996.

N. Revol, K. Makino, and M. Berz, Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY, The Journal of Logic and Algebraic Programming, vol.64, issue.1, pp.135-154, 2005.
DOI : 10.1016/j.jlap.2004.07.008
URL : https://hal.archives-ouvertes.fr/inria-00071850

N. S. Nedialkov, K. R. Jackson, and G. F. Corliss, Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999.
DOI : 10.1016/S0096-3003(98)10083-8

J. A. Sandretto and A. Chapoutot, Validated explicit and implicit runge-kutta methods, Reliable Computing, vol.22, p.79, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01243053

N. Ramdani and N. S. Nedialkov, Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques, Nonlinear Analysis: Hybrid Systems, vol.5, issue.2, pp.149-162, 2011.
DOI : 10.1016/j.nahs.2010.05.010
URL : https://hal.archives-ouvertes.fr/hal-00611996

P. Collins and A. Goldsztejn, The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems, Electronic Notes in Theoretical Computer Science, vol.223, pp.87-102, 2008.
DOI : 10.1016/j.entcs.2008.12.033

E. Goubault, O. Mullier, S. Putot, and M. Kieffer, Inner approximated reachability analysis, Proceedings of the 17th international conference on Hybrid systems: computation and control, HSCC '14, pp.163-172, 2014.
DOI : 10.1145/2562059.2562113
URL : https://hal.archives-ouvertes.fr/hal-01073731

L. Jaulin, Nonlinear bounded-error state estimation of continuous-time systems, Automatica, vol.38, issue.6, pp.1079-1082, 2002.
DOI : 10.1016/S0005-1098(01)00284-9
URL : https://hal.archives-ouvertes.fr/hal-00845483

W. Tucker, The lorenz attractor exists, Comptes Rendus de l'Académie des Sciences -Series I, Mathematics, vol.328, issue.12, pp.1197-1202, 1999.

A. Goldsztejn, W. Hayes, and P. Collins, Tinkerbell Is Chaotic, SIAM Journal on Applied Dynamical Systems, vol.10, issue.4, pp.1480-1501, 2011.
DOI : 10.1137/100819011
URL : https://hal.archives-ouvertes.fr/hal-00835176

P. Van-hentenryck, L. Michel, and Y. Deville, Numerica: a modeling language for global optimization, 1997.

C. Bessiere, Constraint Propagation, Foundations of Artificial Intelligence, vol.2, pp.29-83, 2006.
DOI : 10.1016/S1574-6526(06)80007-6
URL : https://hal.archives-ouvertes.fr/lirmm-00117128

A. K. Mackworth, Consistency in networks of relations, Consistency in networks of relations, pp.99-118, 1977.
DOI : 10.1016/0004-3702(77)90007-8

I. Araya, G. Trombettoni, and B. Neveu, A Contractor Based on Convex Interval Taylor, International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming, pp.1-16, 2012.
DOI : 10.1007/978-3-642-29828-8_1
URL : https://hal.archives-ouvertes.fr/hal-00733848

F. Le-bars, J. Sliwka, L. Jaulin, and O. Reynet, Set-membership state estimation with fleeting data, Automatica, vol.48, issue.2, pp.381-387, 2012.
DOI : 10.1016/j.automatica.2011.11.004
URL : https://hal.archives-ouvertes.fr/hal-00670459

A. Bethencourt and L. Jaulin, Solving Non-Linear Constraint Satisfaction Problems Involving Time-Dependant Functions, Mathematics in Computer Science, vol.4, issue.4, pp.503-523, 2014.
DOI : 10.1007/s11786-014-0209-6

L. Jaulin, Applied interval analysis: with examples in parameter and state estimation, robust control and robotics, 2001.
DOI : 10.1007/978-1-4471-0249-6
URL : https://hal.archives-ouvertes.fr/hal-00845131

S. Veres, Error Control in Polytope Computations, Journal of Optimization Theory and Applications, vol.22, issue.2, pp.325-355, 2002.
DOI : 10.1023/A:1014835026141
URL : http://eprints.soton.ac.uk/22270/1/22270.pdf

V. Drevelle and P. Bonnifait, Localization Confidence Domains via Set Inversion on Short-Term Trajectory, IEEE Transactions on Robotics, vol.29, issue.5, pp.1244-1256, 2013.
DOI : 10.1109/TRO.2013.2262776
URL : https://hal.archives-ouvertes.fr/hal-00877443

G. Chabert and L. Jaulin, Contractor programming, Artificial Intelligence, vol.173, issue.11, pp.1079-1100, 2009.
DOI : 10.1016/j.artint.2009.03.002
URL : https://hal.archives-ouvertes.fr/hal-00428957

A. Kurzhanski and I. Valyi, Ellipsoidal calculus for estimation and control, 1997.
DOI : 10.1007/978-1-4612-0277-6

M. Milanese, J. Norton, H. Piet-lahanier, and ´. E. Walter, Bounding approaches to system identification, 2013.
DOI : 10.1007/978-1-4757-9545-5

C. Aubry, R. Desmare, and L. Jaulin, Loop detection of mobile robots using interval analysis, Automatica, vol.49, issue.2, p.463, 2013.
DOI : 10.1016/j.automatica.2012.11.009
URL : https://hal.archives-ouvertes.fr/hal-00773530

M. Nehmeier and J. W. Gudenberg, filib++ , expression templates and the coming interval standard, Reliable Computing, vol.15, pp.312-320, 2011.
DOI : 10.1007/s00607-011-0176-6

L. E. Dubins, On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents, American Journal of Mathematics, vol.79, issue.3, pp.497-516, 1957.
DOI : 10.2307/2372560

J. Norton and S. M. Veres, Outliers in bound-based state estimation and identification, in: Circuits and Systems, ISCAS'93 IEEE International Symposium on, pp.790-793, 1993.
DOI : 10.1109/iscas.1993.692763

D. Bertsekas and I. Rhodes, Recursive state estimation for a set-membership description of uncertainty, IEEE Transactions on Automatic Control, vol.16, issue.2, pp.117-128, 1971.
DOI : 10.1109/TAC.1971.1099674

A. Gning, S. Julier, and L. Mihaylova, Non-linear state estimation using imprecise samples, Proceedings of the 16th International Conference on Information Fusion, pp.2110-2116, 2013.

T. I. Fossen, Guidance and control of ocean vehicles, 1994.

V. Drevelle and J. Nicola, VIBes: A Visualizer for Intervals and Boxes, Mathematics in Computer Science, vol.8, issue.3-4, pp.563-572, 2014.
DOI : 10.1007/s11786-014-0202-0
URL : https://hal.archives-ouvertes.fr/hal-01090043