M. Althoff, C. Le-guernic, B. H. Krogh, and B. H. Krogh, Reachable set computation for uncertain time-varying linear systems, Proceedings of the 14th international conference on Hybrid systems: computation and control, HSCC '11, pp.93-102, 2011.
DOI : 10.1145/1967701.1967717

M. Althoff, O. Stursberg, and M. Buss, Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization, 2008 47th IEEE Conference on Decision and Control, 2008.
DOI : 10.1109/CDC.2008.4738704

R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P. Ho et al., The algorithmic analysis of hybrid systems, Theoretical Computer Science, vol.138, issue.1, pp.3-34, 1995.
DOI : 10.1016/0304-3975(94)00202-T

R. Alur, C. Courcoubetis, T. A. Henzinger, P. Ho, and P. Ho, Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, Hybrid Systems, pp.209-229, 1992.
DOI : 10.1007/3-540-57318-6_30

R. Alur, T. Dang, F. Ivancic, and F. Ivancic, Progress on Reachability Analysis of Hybrid Systems Using Predicate Abstraction, HSCC, pp.4-19, 2003.
DOI : 10.1007/3-540-36580-X_4

R. Alur, T. Dang, F. Ivancic, and F. Ivancic, Predicate abstraction for reachability analysis of hybrid systems, pp.152-199, 2006.

R. Alur, A. Itai, and R. P. Kurshan, Mihalis Yannakakis, and Mihalis Yannakakis. Timing verification by successive approximation, pp.142-157, 1995.

H. Anai, V. Weispfenning, and V. Weispfenning, Reach Set Computations Using Real Quantifier Elimination, HSCC, pp.63-76, 2001.
DOI : 10.1007/3-540-45351-2_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.4570

E. Asarin, O. Bournez, T. Dang, and O. Maler, Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems, 2000.
DOI : 10.1007/3-540-46430-1_6

URL : https://hal.archives-ouvertes.fr/inria-00099316

E. Asarin, O. Bournez, and T. Dang, Oded Maler, and Oded Maler Approximate reachability analysis of piecewise-linear dynamical systems, 2000.

E. Asarin, T. Dang, and A. Girard, Reachability Analysis of Nonlinear Systems Using Conservative Approximation, HSCC, pp.20-35, 2003.
DOI : 10.1007/3-540-36580-X_5

E. Asarin, T. Dang, A. Girard, and A. Girard, Hybridization methods for the analysis of nonlinear systems, Acta Informatica, vol.12, issue.2, pp.451-476, 2007.
DOI : 10.1007/s00236-006-0035-7

URL : https://hal.archives-ouvertes.fr/hal-00157475

E. Asarin and T. Dang, Oded Maler, and Oded Maler The d/dt tool for verification of hybrid systems, CAV, pp.365-370, 2002.

E. Asarin and T. Dang, Oded Maler, Romain Testylier, and Romain Testylier. Using redundant constraints for refinement, 2011.

D. Avis, K. Fukuda, and K. Fukuda, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra, Discrete & Computational Geometry, vol.8, issue.3, pp.295-313, 1992.
DOI : 10.1007/BF02293050

T. Ball, S. K. Rajamani, and S. K. Rajamani, Bebop: A Symbolic Model Checker for Boolean Programs, SPIN, pp.113-130, 2000.
DOI : 10.1007/10722468_7

T. Ball, S. K. Rajamani, and S. K. Rajamani, The slam project: debugging system software via static analysis, POPL, pp.1-3, 2002.

G. Batt, B. Yordanov, and R. Weiss, Calin Belta, and Calin Belta. Robustness analysis and tuning of synthetic gene networks, pp.2415-2422, 2007.

C. Belta, C. G. Luc, and . Habets, Controlling a Class of Nonlinear Systems on Rectangles, IEEE Transactions on Automatic Control, vol.51, issue.11, pp.1749-1759, 2006.
DOI : 10.1109/TAC.2006.884957

. Marco, A reachability algorithm for multi-affine systems with applications to biological systems, HSCC, pp.76-89, 2007.

O. Botchkarev, S. Tripakis, and S. Tripakis, Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations, HSCC, pp.73-88, 2000.
DOI : 10.1007/3-540-46430-1_10

O. Bouissou, E. Goubault, S. Putot, K. Tekkal, F. Védrine et al., HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment, CAV, pp.620-626, 2009.
DOI : 10.1007/978-3-642-02658-4_46

N. F. Britton, N. R. Franks, S. C. Pratt, and T. D. Seeley, Deciding on a new home: how do honeybees agree?, Proceedings of the Royal Society of London Series B -Biological Sciences, pp.1383-1388, 1498.
DOI : 10.1098/rspb.2002.2001

S. A. Cameron and R. K. Culley, Determining the minimum translational distance between two convex polyhedra, Proceedings. 1986 IEEE International Conference on Robotics and Automation, p.48
DOI : 10.1109/ROBOT.1986.1087645

L. Chen, A. Miné, J. Wang, P. Cousot, and P. Cousot, Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships, SAS, pp.309-325, 2009.
DOI : 10.1007/0-387-32698-7_2

URL : https://hal.archives-ouvertes.fr/hal-00531564

A. Chutinan, B. H. Krogh, and B. H. Krogh, Computing Approximating Automata for a Class of Linear Hybrid Systems, Hybrid Systems, pp.16-37, 1997.
DOI : 10.1007/3-540-49163-5_2

A. Chutinan, B. H. Krogh, and B. H. Krogh, Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations, HSCC, pp.76-90, 1999.
DOI : 10.1007/3-540-48983-5_10

E. M. Clarke, A. Fehnker, Z. Han, B. H. Krogh, O. Stursberg et al., Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement, TACAS, pp.192-207, 2003.
DOI : 10.1007/3-540-36577-X_14

E. M. Clarke, O. Grumberg, S. Jha, and Y. Lu, Helmut Veith, and Helmut Veith. Counterexample-guided abstraction refinement, CAV, pp.154-169, 2000.

J. C. Corbett, M. B. Dwyer, J. Hatcliff, S. Laubach, C. S. Pasareanu et al., Bandera, Proceedings of the 22nd international conference on Software engineering , ICSE '00, pp.439-448, 2000.
DOI : 10.1145/337180.337234

P. Cousot and R. Cousot, Static determination of dynamic properties of programs, Proc. of the Second Int. Symp. on Programming, pp.106-130, 1976.

T. Dang, Approximate Reachability Computation for Polynomial Systems, In HSCC, pp.138-152, 2006.
DOI : 10.1007/11730637_13

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.7488

T. Dang, T. M. Gawlitza, and T. M. Gawlitza, Template-Based Unbounded Time Verification of Affine Hybrid Automata, APLAS, pp.34-49, 2011.
DOI : 10.1007/978-3-540-24743-2_40

T. Dang, C. L. Guernic, and O. Maler, Computing Reachable States for Nonlinear Biological Models, Computational Methods in Systems Biology, 7th International Conference Proceedings, pp.126-141, 2009.
DOI : 10.1007/978-1-4613-8431-1

T. Dang and O. Maler, Reachability analysis via face lifting, HSCC, pp.96-109, 1998.
DOI : 10.1007/3-540-64358-3_34

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.4435

T. Dang, O. Maler, and R. Testylier, Accurate hybridization of nonlinear systems, Proceedings of the 13th ACM international conference on Hybrid systems: computation and control, HSCC '10, pp.11-20, 2010.
DOI : 10.1145/1755952.1755956

T. Dang, D. Salinas, and D. Salinas, Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion, CAV, pp.219-232, 2009.
DOI : 10.1007/978-3-642-02658-4_19

T. Dang and R. Testylier, Hybridization domain construction using curvature estimation, Proceedings of the 14th international conference on Hybrid systems: computation and control, HSCC '11, pp.123-132, 2011.
DOI : 10.1145/1967701.1967721

T. X. , T. Dang, D. De-l-'inpg, S. Automatique, D. Thi et al., Verification Et, Synthese Des, Systemes Hybrides, Directeur De These, M. Eugene Asarin, M. Pravin Varaiya, and M. Pravin Varaiya. Vérification et synthèse des systèmes hybrides, 2000.
URL : https://hal.archives-ouvertes.fr/tel-00006738

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

I. A. Fotiou, P. Rostalski, P. A. Parrilo, and M. Morari, Parametric optimization and optimal control using algebraic geometriy methods, International Journal of Control, issue.11, pp.791340-1358, 2006.
DOI : 10.1080/00207170600726592

A. Ioannis, P. A. Fotiou, M. Parrilo, M. Morari, and . Morari, Parametric optimization and optimal control using algebraic geometry, 2006.

G. Frehse, C. Le-guernic, A. Donzé, S. Cotton, R. Ray et al., SpaceEx: Scalable Verification of Hybrid Systems, Proc. 23rd International Conference on Computer Aided Verification (CAV), 2011.
DOI : 10.1007/978-3-642-00768-2_32

URL : https://hal.archives-ouvertes.fr/hal-00769608

J. Garloff and A. P. Smith, Rigorous affine lower bound functions for multivariate polynomials and their use in global optimisation, Proceedings of the 1st International Conference on Applied Operational Research , Tadbir Institute for Operational Research, Systems Design and Financial Services, pp.199-211, 2008.

A. Girard, Reachability of Uncertain Linear Systems Using Zonotopes, HSCC, pp.291-305, 2005.
DOI : 10.1007/978-3-540-31954-2_19

URL : https://hal.archives-ouvertes.fr/hal-00307003

A. Girard, C. L. Guernic, and O. Maler, Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs, 2006.
DOI : 10.1007/11730637_21

URL : https://hal.archives-ouvertes.fr/hal-00171555

R. Mark, I. Greenstreet, I. Mitchell, and . Mitchell, Reachability analysis using polygonal projections, HSCC, pp.103-116, 1999.

T. A. Henzinger, P. W. Kopke, and A. Puri, Pravin Varaiya, and Pravin Varaiya. What's decidable about hybrid automata, pp.94-124, 1998.

G. J. Holzmann, M. H. Smith, and M. H. Smith, Automating software feature verification, Bell Labs Technical Journal, vol.5, issue.2, pp.72-87, 2000.
DOI : 10.1002/bltj.2223

J. Garloff and A. P. Smith, An Improved Method for the Computation of Affine Lower Bound Functions for Polynomials, Frontiers in Global Optimization, Series Nonconvex Optimization and Its Applications, pp.135-144, 2004.
DOI : 10.1007/978-1-4613-0251-3_8

J. Garloff and A. P. Smith, A Comparison of Methods for the Computation of Affine Lower Bound Functions for Polynomials, Global Optimization and Constraint Satisfaction, pp.71-85, 2005.
DOI : 10.1007/11425076_6

S. G. Johnson, The NLopt nonlinear optimization package http

I. T. Jolliffe, Principal Component Analysis, 2002.
DOI : 10.1007/978-1-4757-1904-8

D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, Oxford Applied Mathematics and Computer Science, 1987.

S. Kaynama, J. Maidens, M. Oishi, I. M. Mitchell, G. A. Dumont et al., Computing the viability kernel using maximal reachable sets, Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control, HSCC '12, pp.55-64, 2012.
DOI : 10.1145/2185632.2185644

E. K. Kostoukova, State estimation for dynamic systems via parallelotopes: Optimization and parallel computations, Optimization Methods and Software, pp.269-306, 1999.

A. B. Kurzhanski and P. Varaiya, Ellipsoidal Techniques for Reachability Analysis, 2000.
DOI : 10.1007/3-540-46430-1_19

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.379.3135

A. B. Kurzhanski, Pravin Varaiya, and Pravin Varaiya. Ellipsoidal techniques for reachability under state constraints, pp.1369-1394, 2006.

A. A. Kurzhanskiy and P. Varaiya, Ellipsoidal toolbox, 2006.
DOI : 10.1109/cdc.2006.377036

M. Kvasnica, P. Grieder, M. Baotic, M. Morari, and M. Morari, Multi-Parametric Toolbox (MPT), HSCC, pp.448-462, 2004.
DOI : 10.1007/978-3-540-24743-2_30

G. Lafferriere, G. J. Pappas, S. Yovine, and S. Yovine, Symbolic Reachability Computation for Families of Linear Vector Fields, Journal of Symbolic Computation, vol.32, issue.3, pp.231-253, 2001.
DOI : 10.1006/jsco.2001.0472

C. Le, G. , and A. Girard, Reachability analysis of hybrid systems using support functions, 21st International Conference on Computer Aided Verification, pp.540-554, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00769527

M. C. Lin and D. Manocha, Collision and proximity queries, Handbook of Discrete and Computational Geometry, 2003.

O. Maler, Z. Manna, A. Pnueli, and A. Pnueli, From timed to hybrid systems, REX Workshop, pp.447-484, 1991.

A. Miné, A new numerical abstract domain based on differencebound matrices, 2007.

I. M. Mitchell, Scalable calculation of reach sets and tubes for nonlinear systems with terminal integrators, Proceedings of the 14th international conference on Hybrid systems: computation and control, HSCC '11, pp.103-112, 2011.
DOI : 10.1145/1967701.1967718

I. M. Mitchell, R. M. Bayen, and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, vol.50, issue.7, pp.947-957, 2005.
DOI : 10.1109/TAC.2005.851439

I. M. Mitchell, C. Tomlin, and C. Tomlin, Overapproximating reachable sets by hamilton-jacobi projections, pp.323-346, 2003.

B. Mourrain, J. P. Pavone, and J. P. Pavone, Subdivision methods for solving polynomial equations, Journal of Symbolic Computation, vol.44, issue.3, pp.292-306, 2009.
DOI : 10.1016/j.jsc.2008.04.016

URL : https://hal.archives-ouvertes.fr/inria-00070350

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

A. Platzer and J. Quesel, KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description), IJCAR, pp.171-178, 2008.
DOI : 10.1007/978-3-540-71070-7_15

A. Platzer, Differential-algebraic dynamic logic for differentialalgebraic programs, J. Log. Comput, 2008.
DOI : 10.1093/logcom/exn070

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.2188

A. Platzer, E. M. Clarke, and E. M. Clarke, Computing differential invariants of hybrid systems as fixedpoints, CAV, pp.176-189, 2008.

A. Platzer, E. M. Clarke, and E. M. Clarke, Computing differential invariants of hybrid systems as fixedpoints, pp.98-120, 2009.

S. Prajna, Barrier certificates for nonlinear model validation, pp.117-126, 2006.

S. Prajna, A. Jadbabaie, and A. Jadbabaie, Safety Verification of Hybrid Systems Using Barrier Certificates, HSCC, pp.477-492, 2004.
DOI : 10.1007/978-3-540-24743-2_32

S. Prajna, A. Jadbabaie, and G. J. Pappas, A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates, IEEE Transactions on Automatic Control, vol.52, issue.8, pp.1415-1429, 2007.
DOI : 10.1109/TAC.2007.902736

S. Ratschan and Z. She, Safety verification of hybrid systems by constraint propagation-based abstraction refinement, ACM Trans. Embed. Comput. Syst, vol.6, issue.1, 2007.

E. Rodríguez-carbonell, A. Tiwari, and A. Tiwari, Generating Polynomial Invariants for Hybrid Systems, In HSCC, pp.590-605, 2005.
DOI : 10.1007/978-3-540-31954-2_38

S. Boyd and S. Vandenberghe, Convex optimization, 2004.

S. Sankaranarayanan, T. Dang, F. Ivancic, and F. Ivancic, Symbolic Model Checking of Hybrid Systems Using Template Polyhedra, TACAS, pp.188-202, 2008.
DOI : 10.1007/978-3-540-78800-3_14

S. Sankaranarayanan, H. Sipma, Z. Manna, and Z. Manna, Constructing invariants for hybrid systems, In HSCC, pp.539-554, 2004.
DOI : 10.1007/s10703-007-0046-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.2632

S. Sankaranarayanan, H. B. Sipma, Z. Manna, and Z. Manna, Scalable Analysis of Linear Systems Using Mathematical Programming, pp.25-41, 2005.
DOI : 10.1007/978-3-540-30579-8_2

S. Sankaranarayanan, H. B. Sipma, Z. Manna, and Z. Manna, Constructing invariants for hybrid systems, pp.25-55, 2008.
DOI : 10.1007/s10703-007-0046-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.2632

S. Sastry, Nonlinear Systems: Analysis, Stability and Control
DOI : 10.1007/978-1-4757-3108-8

J. R. Shewchuk, What is a good linear element? interpolation , conditioning, and quality measures, 2002.

A. Simon and A. King, Exploiting Sparsity in Polyhedral Analysis, SAS, pp.336-351, 2005.
DOI : 10.1007/11547662_23

A. Stuart and A. R. Humphries, Numerical analysis of dynamical systems, Acta Numerica, vol.25
DOI : 10.1007/BF01385623

O. Stursberg, B. H. Krogh, and B. H. Krogh, Efficient Representation and Computation of Reachable Sets for Hybrid Systems, In HSCC, pp.482-497, 2003.
DOI : 10.1007/3-540-36580-X_35

C. William, B. F. Thibault, and . Naylor, Set operations on polyhedra using binary space partitioning trees, SIGGRAPH Comput. Graph, vol.21, issue.4, 1987.

A. Tiwari, G. Khanna, and G. Khanna, Nonlinear Systems: Approximating Reach Sets, HSCC, pp.600-614, 2004.
DOI : 10.1007/978-3-540-24743-2_40

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.1290

P. Variaya, Reach Set Computation Using Optimal Control, KIT workshop on verification of hybrid systems, 1998.
DOI : 10.1007/978-3-642-59615-5_15