]. P. Bibliography-1, A. Abdulla, A. Annichini, and . Bouajjani, Symb o l i cveriication of lossy channel systems: Application to the bounded retransmission protocol, LNCS, vol.1579, pp.208-222, 1999.

A. D. Aleksandrov, A. N. Kolmogorov, and M. A. Lavrent-'ev, Mathematics: Its content, methods and meaning, 1963.

J. F. Allen and P. J. Hayes, Moments and points in an interval-based temporal logic, Computational Intelligence, vol.2, issue.2, pp.225-238, 1990.
DOI : 10.1016/S0364-0213(82)90003-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.620.5144

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, and P. Ho, Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems, Hybrid Systems, numb e r736 in LNCS, pp.209-229, 1993.
DOI : 10.1007/3-540-57318-6_30

R. Alur and D. L. Dill, A theory of timed automata, Theoretical Computer Science, vol.126, issue.2, pp.183-235, 1994.
DOI : 10.1016/0304-3975(94)90010-8

R. Alur, R. Groshu, Y. Hur, V. Kumar, and I. Lee, Modular speciication of hybrid systems in charon, LNCS, vol.1790, issue.00, pp.6-19, 2000.

R. Alur, T. A. Henzinger, and P. Ho, Automatic symbolic veriication of embedded systems, IEEE Transactions on Software Engineering, 1996.
DOI : 10.1109/real.1993.393520
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.181

R. Alur and T. A. Henzinger, Logics and models of real time: A survey, Real Time: Theory in Practice, pp.74-106, 1992.
DOI : 10.1007/BFb0031988

R. Alur, T. A. Henzinger, and M. Y. Vardi, Parametric real-time reasoning, Proceedings of the twenty-fifth annual ACM symposium on Theory of computing , STOC '93, pp.592-601, 1993.
DOI : 10.1145/167088.167242
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.3317

R. Alur, S. Kannan, and S. L. Torre, Polyhedral ows in hybrid automata, HSCC'99, numb e r1569 in LNCS, pp.5-18, 1999.

R. Alur and R. P. Kurshan, Timing analysis in COSPAN, Hybrid Systems III, volume 1066 of LNCS, pp.220-231, 1996.
DOI : 10.1007/BFb0020948

E. Asarin, O. Bournez, T. Dang, and O. Maler, Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems, HSCC'00, numb e r1790 in LNCS, 2000.
DOI : 10.1007/3-540-46430-1_6
URL : https://hal.archives-ouvertes.fr/inria-00099316

E. Asarin and O. Maler, On some relations b e t ween dynamical systems and transition systems, ICALP'94, numb e r820, 1994.

E. Asarin, O. Maler, and A. Pnueli, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, pp.35-65, 1995.
DOI : 10.1016/0304-3975(94)00228-B

G. Asarin, G. Pace, S. Schneider, and . Yovine, SPeeDI ??? A Verification Tool for Polygonal Hybrid Systems, CAV'2002, 2002.
DOI : 10.1007/3-540-45657-0_28
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.5596

E. Asarin and G. Schneider, Widening the boundary b e t ween decidable and undecidable hybrid systems, CONCUR'2002, 2002.
DOI : 10.1007/3-540-45694-5_14
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.7440

E. Asarin, G. Schneider, and S. Yovine, On the decidability of the reachability problem for planar diierential inclusions, HSCC'2001 (Hybrid Systems: Computation and Control), numb e r2034 in LNCS, pp.89-104, 2001.

E. Asarin, G. Schneider, and S. Yovine, Towards computing phase portraits of polygonal diierential inclusions, HSCC'2002 (Hybrid Systems: Computation and Control), numb e r2289 in LNCS, pp.49-61, 2002.

J. Aubin, A Survey of Viability Theory, SIAM Journal on Control and Optimization, vol.28, issue.4, pp.749-789, 1990.
DOI : 10.1137/0328044

J. Aubin, Viability Theory, Birkhh auser, 1991.
DOI : 10.1007/978-3-642-16684-6
URL : https://hal.archives-ouvertes.fr/inria-00636570

J. Aubin, The Substratum of Impulse and Hybrid Control Systems, HSCC'01, pp.105-118, 2001.
DOI : 10.1007/3-540-45351-2_12

J. Aubin and A. Cellina, Diierential Inclusions. Numb e r264 in A Series of Comprehensive Studies in Mathematics, 1984.

J. Aubin, J. Lygeros, M. Quincampoix, and S. Sastry, Impulse diierential inclusions: A viability approach to hybrid systems, IEEE Transactions on Automatic Control, 2002.
DOI : 10.1109/9.981719
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.3599

J. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube, Towards a viability theory for hybrid systems, European Control Conference, 2001.

J. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube, Viability and invariance kernels of impulse diierential inclusions, Conference on Decision and Control, pp.340-345

A. Balluchi, L. Benvenuti, G. M. Miconi, U. Pozzi, T. Villa et al., Maximal safe set computation for idle speed control of an automative engine, LNCS, vol.1790, p.0, 2000.

N. Bauer, S. Kowalewski, and G. Sand, A case study: Multi product batch plant for the demonstration of control and scheduling problems, 2000.

N. Bauer, A demonstration plant for the control and scheduling of multi-product batch operations, VHS Case Study, vol.7, 2000.

J. Bengtsson, K. G. Larsen, F. Larsson, P. Pettersson, and W. Yi, Uppaal | a To o lSuite for Automatic Veriication of Real{Time Systems, Proc. of Workshop on Veriication and Control of Hybrid Systems III, numb e r1066 in LNCS, pp.232-243, 1995.

S. Bensalem, Y. Lakhnech, and S. Owre, Computing abstractions of innnite state systems compositionally and automatically, Computer-Aided Veriication, CAV '98, pp.319-331, 1998.
DOI : 10.1007/bfb0028755
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.104

S. Bensalem, Y. Lakhnech, and S. Owre, InVeSt : A tool for the verification of invariants, Computer-Aided Veriication, CAV '98, pp.505-510, 1998.
DOI : 10.1007/BFb0028771

R. Bird and P. Wadler, Introduction to Functional Programming, 1988.

V. D. Blondel and J. N. Tsitsilkis, Complexity of stability and controllability of elementary hybrid systems, Automatica, vol.35, issue.3, pp.479-489, 1999.
DOI : 10.1016/S0005-1098(98)00175-7

B. Boigelot, P. Godefroid, B. Willems, and P. Wolper, The p o wer of QDDs, SAS'97

B. Boigelot and P. Wolper, Symbolic veriication with periodic sets, Proceedings of the 6th International Conference on Computer Aided Veriication, pp.55-67, 1994.
DOI : 10.1007/3-540-58179-0_43
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.6568

O. Botchkarev and S. Tripakis, Veriication of hybrid systems with linear diierential inclusions using ellipsoidal approximations, HSCC'00, numb e r1790 in LNCS, 2000.

A. Bouajjani, R. Echahed, and R. Robbana, Verifying invariance properties of timed systems with duration variables, Intern. Symp. on Formal Techniques in Real Time and Fault Tolerant Systems (FTRTFT'94), numb e r863 in LNCS Septemb e r1994, pp.193-210
DOI : 10.1007/3-540-58468-4_166

A. Bouajjani and P. Habermehl, Symbolic Reachability Analysis of FIFO Channel Systems with Nonregular Sets of Conngurations (extended abstract), Automata, Languages and Programming, 24th International Colloquium, pp.560-570, 1997.

A. Bouajjani and R. Robbana, Verifying omega-regular properties for a subclass of linear hybrid systems, 7th Intern. Conf. on Computer Aided Veriication (CAV'95), numb e r939 in LNCS, pp.437-450, 1995.

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

P. Bouyer, C. Dufourd, E. Fleury, and A. Petit, Are timed automata updatable?, 12th Int. Conf. Computer Aided Veriication (CAV'2000), pp.464-479, 2000.
DOI : 10.1007/10722167_35
URL : https://hal.archives-ouvertes.fr/hal-00350488

P. Bouyer, C. Dufourd, E. Fleury, and A. Petit, Expressiveness of Updatable Timed Automata, 25th Int. Symp. Math. Found. Comp. Sci. (MFCS'2000), pp.232-242, 2000.
DOI : 10.1007/3-540-44612-5_19
URL : https://hal.archives-ouvertes.fr/hal-00350490

S. Michael and . Branicky, Universal computation and other capabilities of hybrid and continuous dynamical systems, Theoretical Computer Science, vol.138, issue.1, 1995.

F. Brauer and J. A. , The qualitative theory of ordinary diierential equations: an introduction, 1969.

M. Broucke, A geometric approach to bisimulation and veriication of hybrid systems, HSCC'99, numb e r1569 in LNCS, 1999.

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

A. Chutinan and B. H. Krogh, Computing polyhedral approximations to dynamic ow pipes, Proc. of the 37th Annual International Conference on Decision and Control, CDC'98, 1998.
DOI : 10.1109/cdc.1998.758642
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.2098

E. M. Clarke, Orna Grumberg, and Doron A. Peled. Model checking, 1999.

E. M. Clarke and E. A. Emerson, Design and synthesis of synchronization skeletons using branching time temporal logic, Proceedings of the Workshop on Logics of Programs, pp.52-71, 1981.

E. M. Clarke, E. A. Emerson, and A. P. Sistla, Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Transactions on Programming Languages and Systems, vol.8, issue.2, pp.244-263, 1986.
DOI : 10.1145/5397.5399

T. Coquand and G. Huet, The calculus of constructions, Information and Computation, vol.76, issue.2-3, 1988.
DOI : 10.1016/0890-5401(88)90005-3
URL : https://hal.archives-ouvertes.fr/inria-00076024

P. Cousot, Abstract interpretation, ACM Computing Surveys, vol.28, issue.2, pp.324-328, 1996.
DOI : 10.1145/234528.234740
URL : https://hal.archives-ouvertes.fr/inria-00528590

P. Cousot and R. Cousot, Abstract interpretation: a uniied lattice model for static analysis of programs by construction or approximation of xpoints, Conference Record of the Fourth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp.238-252, 1977.

H. C. Cunningham, Notes on functional programming with gofer, 1995.

M. Dam, Temporal Logic, Automata and Classical Theories: an Introduction, 1994. Notes for the Sixth European Summer School in Logic, Language and Information

T. Dang and O. Maler, Reachability analysis via face lifting, HSCC'98, numb e r 1386 in LNCS, pages 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, V eriication et synth ese des syst emes hybrides, 2000.

A. Deshpande and P. Varaiya, Viable control of hybrid systems, Hybrid Systems II, numb e r999 in LNCS, pp.128-147, 1995.

J. , D. Dora, and S. Yovine, Looking for a methodology for analyzing hybrid systems, 2001.

J. J. Fey and J. H. Van-schuppen, VHS case study 4 -modeling and control of a juice processing plant. draft, 1999.

A. J. Field and P. G. Harrison, Functional Programming, 1988.

A. F. Filippov, Diierential equations with discontinuous right-hand side. Sbornik English trans. in Amer, Math. Soc. Translations, vol.542, pp.99-127199, 1960.

A. F. Filippov, Diierential equations with discontinuous righthand sides, Kluwer Acaemic, 1988.

M. R. Greenstreet and I. Mitchell, Reachability Analysis Using Polygonal Projections, HSCC'99, numb e r1569 in LNCS, pages 103{116, 1999.
DOI : 10.1007/3-540-48983-5_12

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Linear Algebra, 1990.

J. Guckenheimer and S. Johnson, Planar hybrid systems, Hybrid Systems and Autonomous Control Workshop, pp.202-225, 1994.
DOI : 10.1007/3-540-60472-3_11

R. Michael, Z. Hansen, /. Chaochen, and P. Iist, Lecture Notes on Logical Foundations for the Duration Calculus, Lecture Notes, vol.13, issue.3058, 1993.

M. Henle, A combinatorial introduction to topology, 1979.

T. A. Henzinger, P. Ho, and H. Wong-toi, HYTECH: the next generation, Proceedings 16th IEEE Real-Time Systems Symposium
DOI : 10.1109/REAL.1995.495196

T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya, What's decidable about hybrid automata?, 27th Annual Symposium on Theory of Computing, pp.373-382, 1995.
DOI : 10.1006/jcss.1998.1581
URL : http://doi.org/10.1006/jcss.1998.1581

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

A. Thomas and . Henzinger, The theory of hybrid automata, 11th Annual IEEE Symposium on Logic in Computer Science, pp.278-292, 1996.

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

H. Hochstadt, Diierential equations: a modern approach, 1963.

G. J. Holzmann, Design and Validation of Computer Protocols, 1991.

G. J. Holzmann and D. Peled, The state of Spin, CAV'96: 8th International Conference on Computer Aided Veriication, pp.385-389, 1996.
DOI : 10.1007/3-540-61474-5_85

J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation, 1979.

G. Huet, G. Kahn, and C. Paulin-mohring, The coq proof assistant -a tutorial, version 6.1, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00069967

S. Peyton, J. , and J. Hughes, Report on Haskell 98: A non-strict, purely functional language, 1999.

Y. Kesten, A. Pnueli, J. Sifakis, and S. Yovine, Integration Graphs: A class of decidable hybrid systems, Hybrid Systems, numb e r736 in LNCS, pp.179-208, 1993.
DOI : 10.1007/3-540-57318-6_29

P. Koiran, My favourite problems

P. Koiran, M. Cosnard, and M. Garzon, Computability with low-dimensional dynamical systems, Theoretical Computer Science, vol.132, issue.1-2, pp.113-128, 1994.
DOI : 10.1016/0304-3975(94)90229-1

P. Koiran and C. Moore, Closed-form analytic maps in one and two dimensions can simulate universal turing machines, Theoretical Computer Science, vol.210, issue.1, pp.217-223, 1999.
DOI : 10.1016/S0304-3975(98)00117-0

A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, 1975.

M. Kourjanski and P. Varaiya, Stability of hybrid systems, Hybrid Systems III, numb e r1066 in LNCS, pp.413-423, 1996.
DOI : 10.1007/BFb0020964

P. Kowalczyk and M. Bernardo, On a Novel Class of Bifurcations in Hybrid Dynamical Systems, HSCC'01, numb e r2034 in LNCS, 2001.
DOI : 10.1007/3-540-45351-2_30

A. B. Kurzhanski and P. Varaiya, Ellipsoidal Techniques for Reachability Analysis, HSCC'00, numb e r1790 in LNCS, 2000.
DOI : 10.1007/3-540-46430-1_19

G. Laaerriere, G. J. Pappas, and S. Yovine, A New Class of Decidable Hybrid Systems, Hybrid Systems : Computation and Control, pp.137-151, 1999.
DOI : 10.1007/3-540-48983-5_15

G. Laaerriere, G. J. Pappas, and S. Sastry, O{Minimal hybrid systems, 1998.

M. Leucker, T. Noll, P. Stevens, and M. Weber, Functional programming languages for veriication tools: Experiences with ML and Haskell, Proceedings of the Scottish Functional Programming Workshop (SFPW'01), 2001.
DOI : 10.1007/s10009-004-0184-3

H. R. Lewis and C. H. Papadimitriou, Elements of the Theory of Computation, 1981.

A. M. Lyapunov, The general problem of stability of motion, p.1892

O. Maler and A. Pnueli, Reachability analysis of planar multi-linear systems, Proceedings of the 4th Computer-Aided Veriication, 1993.
DOI : 10.1007/3-540-56922-7_17

O. Maler and A. Pnueli, Reachability analysis of planar multi-linear systems, Proc. of the 5th Workshop on Computer-Aided Veriication, numb e r697 in LNCS, pp.194-209, 1993.
DOI : 10.1007/3-540-56922-7_17

. Uribe, Step: The stanford temporal prover, TAPSOFT, pp.793-794, 1995.

A. Marchaud, Sur les champs de demi-cones et les equations diierentielles du premier ordre, Bull. Soc. Math. France, p.62, 1934.
DOI : 10.24033/bsmf.1211
URL : http://archive.numdam.org/article/BSMF_1934__62__1_0.pdf

A. Matveev and A. Savkin, Qualitative theory of hybrid dynamical systems, Birkhh auser Boston, 2000.
DOI : 10.1007/978-1-4612-1364-2

L. Kenneth and . Mcmillan, Symbolic Model Checking, 1993.

R. Milner, Communication and Concurrency, 1989.

M. L. Minsky, Computation: Finite and Innnite Machines, 1967.

C. Moore, Unpredictability and undecidability in dynamical systems, Physical Review Letters, vol.64, issue.20, 1990.
DOI : 10.1103/PhysRevLett.64.2354

B. Moszkowski, A temporal logic for multi-level reasoning about hardware, IEEE Computer, vol.2, issue.18, 1985.

V. V. Nemytskii and V. V. Stepanov, Qualitative theory of diierential equations, 1960.

X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, An approach to the description and analysis of hybrid systems, Hybrid Systems, numb e r736 in LNCS, pp.149-178, 1993.
DOI : 10.1007/3-540-57318-6_28

A. Olivero, J. Sifakis, and S. Yovine, Using abstractions for the veriication of linear hybrid systems, 6th Computer-Aided Veriication, CAV'94, numb e r818 in LCNS, pp.81-94, 1994.

S. Owre, J. Rushby, and N. Shankar, PVS : a prototype veriication system, 11th Conf. on Automated Deduction, pp.748-752, 1992.
DOI : 10.1007/3-540-55602-8_217
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.2627

C. H. Papadimitriou, Computational complexity, 1994.

L. C. Paulson, Isabelle: A Generic Theorem Prover, With contributions by Tobias Nipkow), 1994.
DOI : 10.1007/BFb0030541

A. Pnueli, The temporal logic of programs, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp.46-57, 1977.
DOI : 10.1109/SFCS.1977.32

H. Poincar-e, M emoire sur les courbes d eenies par les equations dii erentielles I-IV, Ouvre I

H. Poincar-e, Sur les equations de la dynamique et le probl eme des trois corps, Acta Math, vol.13, pp.1-270, 1890.

H. Poincar-e, Les m ethodes nouvelles de la m ecanique c eleste, 3 Vols

A. N. Prior, Time and Modality, 1957.

A. Puri and P. Varaiya, Decidability of hybrid systems with rectangular diierential inclusions, CAV 94, numb e r818 in LNCS, 1994.

A. Puri, P. Varaiya, and V. Borkar, Epsilon approximations of diierential inclusions, Hybrid Systems III, pp.362-376, 1996.

J. P. Queille and J. Sifakis, A temporal logic to deal with fairness in transition systems, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982), pp.217-225, 1982.
DOI : 10.1109/SFCS.1982.57

S. Raczynski, Diierential inclusion in systems simulation, Trans. of the Society for Computer Simulation, vol.13, issue.1, 1996.

H. Rogers, Theory of recursive functions and eeective computability, 1987.

K. S. Sibirsky, Introduction to Topological Dynamics, 1975.
DOI : 10.1007/978-94-010-2308-5

S. Simi-c, K. Johansson, S. Sastry, and J. Lygeros, Towards a geometric theory of hybrid systems, HSCC'00, numb e r1790, 2000.

C. Stirling, Modal and Temporal Logics, Handbook of Logic in Computer Science. Background: Computational Structures, pp.477-563, 1992.

C. Tomlin, J. Lygeros, and S. Sastry, Connict resolution for air traac management: A study in multi-agent hybrid systems, In Trans. on Automatic Control IEEE, vol.43, 1998.

C. J. Tomlin and M. R. Greenstreet, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, vol.2289, 2002.
DOI : 10.1007/3-540-45873-5

S. Tripakis and C. Courcoubetis, Extending Promela and SPIN for real time Algorithmic problems in analysis of real-time systems speciications, TACAS'96 Cerr ans and J. V ksna. Deciding reachability for planar multi-polynomial systems, 1992.

F. W. Vaandrager and J. H. Van-schuppen, Hybrid Systems : Computation and Control, Lecture Notes in Computer Science, vol.1569, 1999.
DOI : 10.1007/3-540-48983-5

S. Yovine, KRONOS: a??verification tool for real-time systems, International Journal on Software Tools for Technology Transfer, vol.1, issue.1-2, pp.123-133, 1997.
DOI : 10.1007/s100090050009

S. Yovine, Model checking timed automata, Lectures on Embedded Systems, 1998.
DOI : 10.1007/3-540-65193-4_20

S. K. Zaremba, Sur les equations au paratingent, Bull. Sc. Math. France, p.60, 1936.