C. Alexander and T. I. Seidman, Sliding modes in intersecting switching surfaces, Houston J. Math, vol.24, p.5455569, 1994.

C. Alur, N. Courcoubetis, T. A. Halbwachs, P. Henzinger, X. Ho et al., The algorithmic analysis of hybrid systems, Theoretical Computer Science, vol.138, p.3334, 1995.

C. Alur, T. A. Courcoubetis, P. Henzinger, and . Ho, Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, Hybrid Systems, p.2099229, 1993.
DOI : 10.1007/3-540-57318-6_30

D. L. Alur and . Dill, A theory of timed automata, Theoretical Computer Science, vol.126, p.1833235, 1994.

R. Alur, Y. Grosu, V. Hur, I. Kumar, and . Lee, Modular speciication of hybrid systems in CHARON, Hybrid Systems: Computation and Control, p.6619, 2000.

T. A. Alur, G. Henzinger, G. Laaerriere, and . Pappas, Discrete abstractions of hybrid systems, Proc. of the IEEE, 2000.
DOI : 10.1109/5.871304

J. Antsaklis, J. A. Stiver, and M. D. Lemmon, Hybrid system modeling and autonomous control systems, Hybrid Systems, p.3666392, 1993.
DOI : 10.1007/3-540-57318-6_37

S. Asarin, B. Bansal, T. Espiau, O. Dang, and . Maler, On hybrid control of underactuated mechanical systems, p.183, 2000.

O. Asarin, T. Bournez, O. Dang, and . Maler, Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems, Hybrid Systems: Computation and Control, 2000.
DOI : 10.1007/3-540-46430-1_6
URL : https://hal.archives-ouvertes.fr/inria-00099316

O. Asarin, T. Bournez, O. Dang, A. Maler, and . Pnueli, EEective synthesis of switching controllers for linear systems, Proceedings of the IEEE, 2000.

R. N. Asarin and . Izmailov, Determining the sliding speed on a discontinuity surface, Avtomatika Telemekhanika transl., Automation and Remote Control, vol.9, issue.50, p.118111185, 1989.

O. Asarin and . Maler, As Soon as Possible: Time Optimal Control for Timed Automata, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, 1999.
DOI : 10.1007/3-540-48983-5_6

O. Asarin, A. Maler, and . Pnueli, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, p.35566, 1995.
DOI : 10.1016/0304-3975(94)00228-B

O. Asarin, A. Maler, and . Pnueli, Symbolic controller synthesis for discrete and timed systems, Hybrid Systems II, Lecture Notes in Computer Science 999, p.1120, 1995.
DOI : 10.1007/3-540-60472-3_1

O. Asarin, A. Maler, J. Pnueli, and . Sifakis, Controller synthesis for timed automata, IFAC Symposium on System Structure and Control, p.4699474, 1998.

P. Aubin and A. Cellina, Diierential Inclusions: Set-valued Maps and Viability Theory, 1984.

L. Balluchi, G. M. Benvenuti, U. Miconi, T. Pozzi, M. D. Villa et al., Maximal safe set computation for idle speed control of an automative engine, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1790, p.32244, 2000.

B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, The quickhull algorithm for convex hulls, ACM Transactions on Mathematical Software, vol.22, issue.4, p.4699483, 1996.
DOI : 10.1145/235815.235821

T. Behrmann, F. W. Hune, and . Vaandrager, Distributed timed model checking how the search order matters, Computer Aided Veriication, 2000.

F. D. Bemporad and . Torrisi, Inner and outter approximation of polytopes using hyper-rectangles, 2000.

A. Bjorner, E. Browne, A. M. Chang, A. Colon, Z. Kapur et al., STeP: Deductive-algorithmic verification of reactive and real-time systems, Computer Aided Veriication, Lecture Notes in Computer Science, 1996.
DOI : 10.1007/3-540-61474-5_92

O. Botchkarev, Ellipsoidal techniques for veriication of hybrid systems Available at: http:::robotics, 2000.

O. Botchkarev and S. Tripakis, Veriication of hybrid systems with linear diierential inclusions using ellipsoidal approximations, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1790, p.73388, 2000.

. Bournez, Complexit e algorithmique des syst emes dynamiques continus et hybrides, 1999.

O. Bournez, A. Maler, and . Pnueli, Orthogonal Polyhedra: Representation and Computation, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, p.46660, 1999.
DOI : 10.1007/3-540-48983-5_8
URL : https://hal.archives-ouvertes.fr/inria-00098887

S. Branicky, Studies in Hybrid Systems: Modelling, Analysis, and Control, 1995.

S. Branicky, V. S. Borkar, and S. K. Mitter, A uniied framwork for hybrid control, Proc. of the 33rd International Conference on Decision and Control, p.422884234, 1994.

. Caspi, Global simulation via partial diierential equations. Unpublished note, Verimag, 1993.

. Chutinan, Hybrid System Veriication Using Discrete Model Approximations, 1999.

B. H. Chutinan and . Krogh, Veriication of polyhedral invariant hybrid automata using polygonal ow pipe approximations, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, p.76690, 1999.

M. Clarke, O. Grumberg, and D. Long, Veriication tools for nite-state concurrent systems, Proceedings of A Decade of Concurrency: Reeections and Perspectives, REX SchoollSymposium, p.1244175, 1994.

M. Clarke and J. M. Wing, Formal methods: state of the art and future directions, ACM Computing Surveys, vol.28, issue.4, p.6233643, 1996.
DOI : 10.1145/242223.242257
URL : https://hal.archives-ouvertes.fr/hal-00444076

D. Cohen and A. C. Hindmarsh, CVODE, a stiiinonstii o d esolver in C. Computers in Physics BIBLIOGRAPHY 355 P. Cousot and R. Cousot. Abstract interpretation and application to logic programs, Journal of Logic Programming, pp.1388143-1033179, 1992.

E. R. Cury, B. H. Krogh, and T. Niinomi, Synthesis of supervisory controllers for hybrid systems based on approximating automata, IEEE Transactions on Automatic Control, vol.43, issue.4, p.5644568, 1998.
DOI : 10.1109/9.664159

. Van-dalen, Logic and Structure, 1994.

O. Dang and . Maler, Reachability analysis via face lifting, Hybrid Systems: Computation and Control, p.966109, 1998.
DOI : 10.1007/3-540-64358-3_34
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.4435

S. Daws and . Tripakis, Model checking of real-time reachability properties using abstractions Tools and Algorithms for the Construction and Analysis of Systems, TACAS'98, 1998.

A. Edgar, Measure, Topology, and Fractal Geometry, 1995.

C. Espiau and . Canudas-de-wit, Sur la commande orbitale de certains systems m ecaniques sous-action es, BIP, 2000.

Z. Fuchs, B. Kedem, and . Naylor, On visible surface generation by a priori tree structures, Proc. of SIGGRAPH'80, p.1244133, 1980.

G. Oll-u and P. Varaiya, Hybrid dynamical systems, Proc. of the 28th International Conference on Decision and Control, p.270882712, 1989.

. Greene, Graphics Gems IV, chapter Detecting intersection of a rectangular solid and a convex polyhedron, p.74482, 1994.

R. Greenstreet, Verifying safety properties of diierential equations, Computer Aided Veriication, CAV'96, p.2777287, 1996.

R. Greenstreet and I. Mitchell, Integrating projections, Hybrid Systems: Computation and Control, p.15991740, 1998.
DOI : 10.1007/3-540-64358-3_38

R. Greenstreet and I. Mitchell, Reachability Analysis Using Polygonal Projections, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, p.76690, 1999.
DOI : 10.1007/3-540-48983-5_12
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.6873

N. Halbwachs, Delay analysis in synchronous programs, Computer Aided Veriication, CAV'93, p.3333346, 1993.
DOI : 10.1007/3-540-56922-7_28

H. Hardy and E. M. Wright, An introduction to the theory of numbers, Bulletin of the American Mathematical Society, vol.35, issue.6, 1979.
DOI : 10.1090/S0002-9904-1929-04793-1

P. Hartman, Ordinary Diierential Equations, 1964.

A. Henzinger, Hybrid automata with nite bisimulations, Proc. ICALP'95, p.3244335, 1995.

A. Henzinger and P. Ho, A note on abstract interpretation strategies for hybrid automata, Hybrid Systems II, Lecture Notes in Computer Science 999, p.2522264, 1995.
DOI : 10.1007/3-540-60472-3_13

A. Henzinger, P. Ho, and H. Wong-toi, HyTech: A model checker for hybrid systems, Software Tools for Technology Transfer, vol.1, p.1100122, 1997.

A. Henzinger, P. Ho, and H. Wong-toi, Analysis of nonlinear hybrid systems, IEEE Transactions on Automatic Control, vol.43, p.5400554, 1998.

A. Henzinger, B. Horowitz, and R. Majumdar, Rectangular Hybrid Games, Concurrency Theory, CONCUR'99, p.3200335, 1999.
DOI : 10.1007/3-540-48320-9_23
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.2

A. Henzinger, B. Horowitz, R. Majumdar, and H. Wong-toi, Beyond HyTech: Hybrid Systems Analysis Using Interval Numerical Methods, Hybrid Systems: Computation and Control, p.1300144, 2000.
DOI : 10.1007/3-540-46430-1_14

A. Henzinger and P. W. Kopke, Discrete-time control for rectangular hybrid automata, Theoretical Computer Science, vol.221, p.3699392, 1999.

W. Hirsch and S. Smale, Diierential Equations, Dynamical Systems and Linear Algebra, 1974.

. Iserles, A rst course in Numerical Analysis of Diierential Equations, 1996.

. E. Jeannet, P. L. Kalman, M. A. Falb, and . Arbib, Partitionnement dynamique dans l'analyse de relations lin eaires et application a la v eriication de programmes synchrones, Topics in Mathematical System Theory, 1968.

A. Kesten, J. Pnueli, S. Sifakis, and . Yovine, Integration Graphs: A class of decidable hybrid systems, Proc. of Workshop on Theory of Hybrid Systems, p.1799208, 1992.
DOI : 10.1007/3-540-57318-6_29

K. Kostoukova, State estimation for dynamic systems via parallelotopes: Optimization and parallel computations, Optimization Methods and Software, vol.9, p.2699306, 1999.

D. Koutsoukos, P. J. Antsaklis, M. D. Lemmon, and J. A. Stiver, Supervisory control of hybrid systems, Proc. of the IEEE, 2000.
DOI : 10.1109/5.871307

O. Kowalewski, M. Stursberg, H. Fritz, J. Graf, S. Preuig et al., A Case Study in Tool-Aided Analysis of Discretely Controlled Continuous Systems: The Two Tanks Problem, Hybrid Systems V, Lecture Notes in Computer Science 1567, p.1633185, 1999.
DOI : 10.1007/3-540-49163-5_9

A. Krishnan, D. Narkhede, and . Manocha, Representation and computation of Boolean combinations of sculptured models, Proceedings of the eleventh annual symposium on Computational geometry , SCG '95, pp.88-97, 1995.
DOI : 10.1145/220279.220325

P. Kurshan and K. L. Mcmillan, Analysis of digital circuits through symbolic reduction, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.10, issue.11, p.135001371, 1991.
DOI : 10.1109/43.97615

I. Kurzhanski and . Valyi, Ellipsoidal Calculus for Estimation and Control, 1997.
DOI : 10.1007/978-1-4612-0277-6

P. Kurzhanski and . Varaiya, Ellipsoidal Techniques for Reachability Analysis, Hybrid Systems: Computation and Control, p.2022214, 2000.
DOI : 10.1007/3-540-46430-1_19

G. Laaerriere, S. Pappas, and . Yovine, Reachability computation for linear systems, Proc. of the 14th IFAC World Congress, p.7712, 1999.

P. Larsen, W. Pettersson, and . Yi, Uppaal in a nutshell, International Journal on Software Tools for Technology Transfer, vol.1, issue.1-2, 1997.
DOI : 10.1007/s100090050010

D. Lemmon, K. X. He, and I. Markovsky, A tutorial introduction to supervisory hybrid system, 1998.

D. Lemmon, K. X. He, and I. Markovsky, Supervisory hybrid systems, IEEE Control Systems Magazine, vol.19, issue.4, 1999.
DOI : 10.1109/37.777788

C. Lin and D. Manocha, Fast interference detection b e t ween geometric models. The Visual Computer, 1110.

D. N. Lygeros, S. Godbole, and . Sastry, Optimal control approach to multiagent, hierarchical system veriication, Proc. of IFAC World Congress, 1996.

K. H. Lygeros, M. Johansson, S. Egerstedt, and . Sastry, On the existence of executions of hybrid automata, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1999.
DOI : 10.1109/CDC.1999.831255

C. Lygeros, S. Tomlin, and . Sastry, Multiobjective hybrid controller synthesis, Proc. International Workshop on Hybrid and Real-Time Systems, Lecture Notes in Computer Science 1201, p.1099123, 1997.
DOI : 10.1007/BFb0014720
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.3955

C. Lygeros, S. Tomlin, and . Sastry, Controllers for reachability speciications for hybrid systems, Automatica, p.35, 1999.

A. Macki and . Strauss, Introduction to Optimal Control Theory, 1982.
DOI : 10.1007/978-1-4612-5671-7

. Maler, A uniied approach for studying discrete and continuous dynamical systems, Proc. of the 37th Annual International Conference on Decision and Control, CDC'98. IEEE, 1998.

Z. Maler, A. Manna, and . Pnueli, From timed to hybrid systems, Real-Time: Theory in Practice, p.4477484, 1992.

A. Maler, J. Pnueli, and . Sifakis, On the synthesis of discrete controllers for timed systems, Proc. STACS'95, p.2299242, 1995.
DOI : 10.1007/3-540-59042-0_76

A. Manna and . Pnueli, Temporal Veriication of Reactive Systems: Safety, 1995.

. L. Mcmillan, Symbolic Model Checking. Kluwer Academic, 1993.

S. Mehlhorn and . Naher, The LEDA Platform of Combinatory and Geometric Computing, 1999.

C. Mitchell and . Tomlin, Level Set Methods for Computation in Hybrid Systems, Hybrid Systems: Computation and Control, p.3111323, 2000.
DOI : 10.1007/3-540-46430-1_27

J. Moor and . Raisch, Discrete control of switched linear systems, Proc. ECC'99, 1999.

S. Morse, Control Using Logic-Based Switching, Control -An European Perspective, 1995.
DOI : 10.1007/978-1-4471-3061-1_4

W. Nerode and . Kohn, Models for hybrid systems, Hybrid Systems, p.3177356, 1993.

X. Nicolin, A. Olivero, J. Sifakis, and S. Yovine, An approach to the description and analysis of hybrid automata, Hybrid Systems, p.1499178, 1993.

G. Pappas, S. Laaerriere, and . Yovine, A new class of decidable hybrid systems, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, p.29931, 1999.

B. O. Pettit, The analysis of piecewise linear dynamical systems, 1995.
DOI : 10.1007/BFb0036083

S. Phillips, T. Levy, and . Munzner, Geomview: An interactive geometry viewer. Notices of the, 1993.

V. Puri, P. Borkar, and . Varaiya, -approximation of diierential inclusions, Hybrid Systems III, Lecture Notes in Computer Science 1066, p.3622376, 1996.
URL : https://hal.archives-ouvertes.fr/in2p3-00000656

P. Puri and . Varaiya, Decidability of hybrid systems with rectangular diierential inclusions, Computer Aided Veriication, CAV'94, p.544104, 1994.

P. Puri and . Varaiya, Driving safely in smart cars, Proceedings of 1995 American Control Conference, ACC'95, 1995.
DOI : 10.1109/ACC.1995.533807

P. Puri and . Varaiya, Veriication of hybrid systems using abstraction, Hybrid Systems II, 1995.

J. Ramadge and W. M. Wonham, The control of discrete event systems, Proc. of the IEEE, 1989.
DOI : 10.1109/5.21072

J. Samet, Design and Analysis of Spatial Data Structure: Quadtree, Octree, and Other Hierachical Methods, 1989.

V. D. Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences, vol.251, 1999.

A. Sethian, Level Set Methods : Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science, 1996.

G. J. Shakernia, S. Pappas, and . Sastry, Decidable Controller Synthesis for Classes of Linear Systems, Hybrid Systems: Computation and Control, p.4077420, 0191.
DOI : 10.1007/3-540-46430-1_34

S. Stursberg and . Kowalewski, Approximating switched continuous systems by rectangular automata, Proc. ECC'99, 1999.

S. Stursberg, S. Kowalewski, and . Engell, Generating timed discrete models of continuous systems, Proc. 2nd IMACS Symposium on Mathematical Modelling, MATHMOD'97, p.2033209, 1997.

S. Stursberg, S. Kowalewski, and . Engell, On the Generation of Timed Discrete Approximations for Continuous Systems, Mathematical and Computer Modelling of Dynamical Systems, vol.6, issue.1, p.51170, 2000.
DOI : 10.1076/1387-3954(200003)6:1;1-Q;FT051

B. Tittus and . Egardt, Controllability and control-law synthesis of linear hybrid systems, Proc. International Conference on Analysis and Optimization of Systems, p.3777383, 1994.
DOI : 10.1007/BFb0033569

J. Tomlin, S. Lygeros, and . Sastry, Connict resolution for air traac management: A study in multi-agent hybrid systems, IEEE Trans. on Automatic Control, vol.434, 1998.

J. Tomlin, S. Lygeros, and . Sastry, A game theoretic approach to controller design for hybrid systems, Proc. of the IEEE, 2000.
DOI : 10.1109/5.871303

I. Utkin, Sliding Modes and their Application in Variable Structure Systems, 1978.

. Varaiya, Reach Set Computation Using Optimal Control, Proc. KIT Workshop, p.3777383, 1998.
DOI : 10.1007/978-3-642-59615-5_15

. Veliov, On the Time-Discretization of Control Systems, 1166 C. Walnum. 3D Graphics Programming with OpenGL. Que Corp, p.147001486, 1995.
DOI : 10.1137/S0363012995288987

. Weiler, Topological Structures for Geometric Modeling, Dept. Comput. Syst. Engr., Rensselaer Polytechnic Inst, 1986.

. Wong-toi, The synthesis of controllers for linear hybrid automata, Proceedings of the 36th IEEE Conference on Decision and Control, 1997.
DOI : 10.1109/CDC.1997.649708

G. Wong-toi and . Hoomann, The control of dense real-time discrete event systems, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1992.
DOI : 10.1109/CDC.1991.261658

K. H. Zhang, S. Johansson, and . Sastry, Dynamical Systems Revisited: Hybrid Systems with Zeno Executions, Hybrid Systems: Computation and Control, p.4511464, 2000.
DOI : 10.1007/3-540-46430-1_37
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.9240

. Zhao, Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based on Phase-space Knowledge, 1992.