A. Açikmese, J. M. Carson, I. , and L. Blackmore, Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem, Table 9.2: Stolfi example, pp.2104-2113, 2013.
DOI : 10.1109/TCST.2012.2237346

[. Baudin, J. Filliâtre, C. Marché, B. Monate, Y. Moy et al., ACSL: ANSI/ISO C Specification Language, pp.13-115

A. Adjé, P. Garoche, and A. Werey, Quadratic Zonotopes -An Extension of Zonotopes to Quadratic Arithmetics In: Programming Languages and Systems -13th Asian Symposium, pp.127-145, 2015.

A. Adjé, S. Gaubert, and E. Goubault, Coupling Policy Iteration with Semi-definite Relaxation to Compute Accurate Numerical Invariants in Static Analysis, Lecture Notes in Computer Science, vol.6012, issue.63, pp.23-42, 2010.
DOI : 10.1007/978-3-642-11957-6_3

A. Amir, R. M. Ahmadi, and . Jungers, Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming In: CDC'13, pp.727-732, 2013.

A. Allamigeon, S. Gaubert, E. Goubault, S. Putot, and N. Stott, A scalable algebraic method to infer quadratic invariants of switched systems, 2015 International Conference on Embedded Software, EMSOFT 2015, pp.75-84, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01423744

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford mathematical monographs Autres tirages, p.121, 2000.

D. Erling, K. D. Andersen, and . Andersen, The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm English In: High Performance Optimization Applied Optimization, pp.197-232, 2000.

A. W. Appel, Verified Software Toolchain -(Invited Talk) Held as Part of the Joint European Conferences on Theory and Practice of Software, Programming Languages and Systems -20th European Symposium on Programming, pp.978-981, 2011.

K. J. , A. , and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, pp.691135762-9780691135762, 2008.

E. M. Aylward, P. A. Parrilo, J. , and E. Slotine, Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming, Automatica, vol.44, issue.8, p.120, 2008.
DOI : 10.1016/j.automatica.2007.12.012

C. Barrett and C. Tinelli, CVC3, Proceedings of the 19 th International Conference on Computer Aided Verification, pp.298-302, 2007.
DOI : 10.1007/978-3-540-73368-3_34

A. Bibliography-[-bau+02-]-patrick-baudin, J. Pacalet, D. Raguideau, N. Schoen, and . Williams, CAVEAT: A Tool for Software Validation, 2002 International Conference on Dependable Systems and Networks, pp.23-26, 2002.

M. A. , B. Sassi, R. Testylier, T. Dang, and A. Girard, Reachability Analysis of Polynomial Systems Using Linear Programming Relaxations In: ATVA 2012 (2012), pp.137-151978

[. Biernacki, J. Colaço, G. Hamon, and M. Pouzet, Clock-directed modular code generation for synchronous data-flow languages, In: LCTES, vol.113, p.77, 2008.

P. Biswas, P. Grieder, J. Löfberg, and M. Morari, A SURVEY ON STABILITY ANALYSIS OF DISCRETE-TIME PIECEWISE AFFINE SYSTEMS, IFAC World Congress. Prague, Czech Republic, p.44, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00332

[. Blackmore, B. Açikmese, J. M. Carson, and I. , Lossless convexification of control constraints for a class of nonlinear optimal control problems In: Systems & Control Letters 61, p.127, 2012.

D. Vincent, O. Blondel, P. Bournez, C. H. Koiran, J. N. Papadimitriou et al., Deciding Stability and Mortality of Piecewise Affine Dynamical Systems, In: Theoretical Computer Science A, pp.1-2, 2001.

M. Bodson, Evaluation of optimization methods for control allocation, In: Journal of Guidance, Control, and Dynamics, vol.254, pp.703-711, 2002.

S. Bonnabel, J. , and E. Slotine, A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter, IEEE Transactions on Automatic Control, vol.60, issue.2, p.120, 2015.
DOI : 10.1109/TAC.2014.2336991

B. Borchers, CSDP, A C library for semidefinite programming, Optimization Methods and Software, vol.6, issue.1-4, pp.1-4, 1999.
DOI : 10.1145/292395.292412

[. Bouissou, E. Goubault, S. Putot, K. Tekkal, and F. Védrine, HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment, Computer Aided Verification, 21st International Conference, pp.620-626978, 2009.
DOI : 10.1007/978-3-642-02658-4_46

T. Bourke and M. Pouzet, Z??lus, Proceedings of the 16th international conference on Hybrid systems: computation and control, HSCC '13, pp.113-1182461348, 2013.
DOI : 10.1145/2461328.2461348

S. Boyd and L. Vandenberghe, Convex optimization, pp.32-36, 2004.

A. Bradley, Understanding IC3, pp.1-14
DOI : 10.1007/978-3-642-31612-8_1

D. Cachera, T. P. Jensen, A. Jobin, and F. Kirchner, Inference of polynomial invariants for imperative programs: A farewell to Gr??bner bases, Science of Computer Programming, vol.93, pp.89-109, 2014.
DOI : 10.1016/j.scico.2014.02.028

L. Stephen, J. Campbell, R. Chancelier, and . Nikoukhah, Modeling and Simulation in Scilab, Scicos, p.78, 2006.

P. Caspi, A. Curic, A. Maignan, C. Sofronis, and S. Tripakis, Translating Discrete-Time Simulink to Lustre, Lecture Notes in Computer Science, vol.2855, pp.84-99, 2003.
DOI : 10.1007/978-3-540-45212-6_7

P. Caspi, D. Pilaud, N. Halbwachs, and J. Plaice, Lustre: A Declarative Language for Programming Synchronous Systems, pp.178-188, 1987.

[. Champion, R. Delmas, and M. Dierkes, Generating property-directed potential invariants by quantifier elimination in a k-induction-based framework, Science of Computer Programming, vol.103, pp.71-87, 2015.
DOI : 10.1016/j.scico.2014.10.004

A. Cimatti, Application of SMT solvers to hybrid system verification In: Formal Methods in Computer-Aided Design, FMCAD 2012, IEEE, p.119, 2012.

M. Colón and S. Sankaranarayanan, Generalizing the Template Polyhedral Domain, In: ESOP. LNCS, vol.75, issue.9, pp.176-195, 2011.
DOI : 10.1007/3-540-45013-0_7

L. D. Joao, J. Comba, and . Stolfi, Affine Arithmetic and its Applications to Computer Graphics, pp.93-100, 1993.

E. Con+08-]-sylvain-conchon, J. Contejean, S. Kanig, and . Lescuyer, CC(X): Semantic Combination of Congruence Closure with Solvable Theories, Electronic Notes in Theoretical Computer Science, vol.198, issue.2, pp.51-69, 2008.
DOI : 10.1016/j.entcs.2008.04.080

A. Costan, S. Gaubert, E. Goubault, M. Martel, and S. Putot, A Policy Iteration Algorithm for Computing Fixed Points in Static Analysis of Programs, Ed. by Kousha Etessami and Sriram K. Rajamani. LNCS, vol.3576, issue.63, pp.462-475, 2005.
DOI : 10.1007/11513988_46

P. Cousot, Proving Program Invariance and Termination by Parametric Abstraction, Lagrangian Relaxation and Semidefinite Programming Lecture Notes in Computer Science, English. In: Verification, Model Checking, and Abstract Interpretation . Ed. by Radhia Cousot, pp.978-981, 2005.

P. Cousot and R. Cousot, Abstract interpretation, Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '77, pp.238-252, 1977.
DOI : 10.1145/512950.512973
URL : https://hal.archives-ouvertes.fr/hal-01108790

P. Cousot and R. Cousot, Abstract Interpretation Frameworks, Journal of Logic and Computation, vol.2, issue.4, pp.511-547, 1992.
DOI : 10.1093/logcom/2.4.511

P. Cousot and R. Cousot, Systematic design of program analysis frameworks, Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '79, pp.269-282, 1979.
DOI : 10.1145/567752.567778

[. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné et al., Combination of Abstractions in the ASTR??E Static Analyzer, LNCS, vol.19, pp.1-24, 2007.
DOI : 10.1007/978-3-540-24725-8_2

[. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné et al., The ASTRÉE Analyser, In: ESOP. LNCS, vol.3444, issue.92, pp.21-30, 2005.

P. Cuoq, F. Kirchner, N. Kosmatov, V. Prevosto, J. Signoles et al., Frama-C, pp.233-247, 2012.
DOI : 10.1007/978-3-642-33826-7_16

[. Damouche, M. Martel, and A. Chapoutot, Transformation of a PID Controller for Numerical Accuracy, Electronic Notes in Theoretical Computer Science, vol.317, pp.47-54, 2015.
DOI : 10.1016/j.entcs.2015.10.006
URL : https://hal.archives-ouvertes.fr/hal-01255942

[. Deters, A. Reynolds, T. King, C. W. Barrett, and C. Tinelli, A tour of CVC4: How it works, and how to use it In: Formal Methods in Computer-Aided Design, IEEE, p.11, 2014.

A. Dieumegard, P. Garoche, T. Kahsai, A. Tailliar, and X. Thirioux, Compilation of synchronous observers as code contracts, Proceedings of the 30th Annual ACM Symposium on Applied Computing, SAC '15, pp.1933-1939, 2015.
DOI : 10.1145/2695664.2695819

[. Dijkstra, A Discipline of Programming, p.13, 1976.

C. John and . Doyle, Analysis of feedback systems with structured uncertainties In: IEE Proceedings D -Control Theory and Applications 129, p.72, 1982.

B. Dutertre, Yices??2.2, Proceedings. Ed. by Armin Biere and Roderick Bloem. Lecture Notes in Computer Science, vol.8559, issue.2, pp.737-744978, 2014.
DOI : 10.1007/978-3-319-08867-9_49

B. Dutertre and L. De-moura, The YICES SMT Solver, Tech. rep. SRI International, issue.11, 2006.

J. Feret, Analysis of Mobile Systems by Abstract Interpretation, p.17, 2005.
URL : https://hal.archives-ouvertes.fr/pastel-00001303

J. Feret, Numerical Abstract Domains for Digital Filters In: International workshop on Numerical and Symbolic Abstract Domains (NSAD), p.56, 2005.

J. Feret, Static Analysis of Digital Filters Held as Part of the Joint European Conferences on Theory and Practice of Software, 13th European Symposium on Programming Proceedings. Ed. by David A, 2004.

. Schmidt, Lecture Notes in Computer Science, pp.33-48978, 2004.

É. Féron, From Control Systems to Control Software, IEEE Control Systems Magazine, vol.30, issue.6, pp.21-82, 2010.
DOI : 10.1109/MCS.2010.938196

J. Filliâtre and C. Marché, The Why/Krakatoa/Caduceus Platform for Deductive Program Verification, Computer Aided Verification, 19th International Conference Proceedings, pp.978-981, 2007.
DOI : 10.1007/978-3-540-73368-3_21

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

R. W. Floyd, Assigning meanings to programs, In: Proceedings of Symposium on Applied Mathematics, vol.19, issue.8, pp.19-32, 1967.
DOI : 10.1090/psapm/019/0235771

G. F. Franklin, M. L. Workman, and D. Powell, Digital Control of Dynamic Systems. 2nd, p.201820544, 1990.

P. Garoche, Static Analysis of Actors by Abstract Interpretation, INPT, p.17, 2008.

P. Garoche, A. Gurfinkel, and T. Kahsai, Synthesizing Modular Invariants for Synchronous Code, Electronic Proceedings in Theoretical Computer Science, vol.169, pp.19-30, 2014.
DOI : 10.4204/EPTCS.169.4

P. Garoche, F. Howar, T. Kahsai, and X. Thirioux, Testing-Based Compiler Validation for Synchronous Languages, NASA Formal Methods -6th International Symposium, NFM 2014 Proceedings, pp.246-251, 2014.
DOI : 10.1007/978-3-319-06200-6_19

P. Garoche, T. Kahsai, and C. Tinelli, Invariant stream generators using automatic abstract transformers based on a decidable logic, pp.3758-3772

P. Garoche, X. Thirioux, and T. Kahsai, LustreC: a modular Lustre compiler. 2012?. url: https://github.com/coco-team/lustrec, p.77

S. Gaubert, E. Goubault, A. Taly, and S. Zennou, Static Analysis by Policy Iteration on Relational Domains, LNCS, vol.4421, issue.63, pp.237-252, 2007.
DOI : 10.1007/978-3-540-71316-6_17

T. Martin, G. , and H. Seidl, Computing Relaxed Abstract Semantics w.r.t. Quadratic Zones Precisely In: SAS, LNCS, vol.6337, issue.64, pp.271-286, 2010.

[. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, and E. Goubault, Abstract interpretation meets convex optimization, Journal of Symbolic Computation, vol.47, issue.12, pp.1416-1446, 2012.
DOI : 10.1016/j.jsc.2011.12.048
URL : https://hal.archives-ouvertes.fr/hal-00778070

T. Gawlitza and H. Seidl, Precise Fixpoint Computation Through Strategy Iteration, LNCS, vol.4421, pp.300-315, 2007.
DOI : 10.1007/978-3-540-71316-6_21
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.153

T. Gawlitza and H. Seidl, Precise Relational Invariants Through Strategy Iteration, LNCS, vol.4646, pp.23-40, 2007.
DOI : 10.1007/978-3-540-74915-8_6

[. Ghorbal, E. Goubault, and S. Putot, A Logical Product Approach to Zonotope Intersection, pp.212-226, 2010.
DOI : 10.1007/978-3-642-14295-6_22

K. Ghorbal, E. Goubault, and S. Putot, The Zonotope Abstract Domain Taylor1+, In: CAV. LNCS, vol.5643, issue.101, pp.627-633, 2009.
DOI : 10.1007/978-3-642-02658-4_47

K. Ghorbal, F. Ivan?i´ivan?i´c, G. Balakrishnan, N. Maeda, and A. Gupta, Donut Domains: Efficient Non-convex Domains for Abstract Interpretation, Model Checking, and Abstract Interpretation -13th International Conference, VMCAI 2012, pp.235-250978, 2012.
DOI : 10.1007/978-3-540-69738-1_20

G. Elmer, I. V. Gilbert, and . Kolmanovsky, Set-point control of nonlinear systems with state and control constraints: a Lyapunov-function, reference-governor approach, Proceedings of the 38th IEEE Conference on, pp.2507-2512, 1999.

J. Gilbert, Éléments d'optimisation différentiable, p.32, 2013.

[. Glover, G. Vinnicombe, and G. Papageorgiou, Guaranteed multi-loop stability margins and the gap metric, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.4084-4085, 2000.
DOI : 10.1109/CDC.2000.912354

E. Goubault, Static Analyses of the Precision of Floating-Point Operations, Proceedings of the 8th International Symposium on Static Analysis. SAS '01, pp.234-259, 2001.
DOI : 10.1007/3-540-47764-0_14

E. Goubault, Static Analysis by Abstract Interpretation of Numerical Programs and Systems, and FLUCTUAT, pp.1-3
DOI : 10.1007/978-3-642-38856-9_1

E. Goubault, T. L. Gall, and S. Putot, An Accurate Join for Zonotopes, Preserving Affine Input/Output Relations, Electronic Notes in Theoretical Computer Science, vol.287, pp.65-76, 2012.
DOI : 10.1016/j.entcs.2012.09.007

E. Goubault and S. Putot, A zonotopic framework for functional abstractions, Formal Methods in System Design, vol.2, issue.1???4, pp.1763-96, 2009.
DOI : 10.1007/s10703-015-0238-z

E. Goubault and S. Putot, Static Analysis of Finite Precision Computations, LNCS, vol.30, issue.3, pp.232-247, 2011.
DOI : 10.1007/978-3-540-24738-8_18

E. Goubault, S. Putot, and F. Védrine, Modular Static Analysis with Zonotopes, In: SAS. LNCS. Springer, vol.7460, issue.101, pp.24-40, 2012.
DOI : 10.1007/978-3-642-33125-1_5

M. Wassim, V. Haddad, and . Chellaboina, Nonlinear Dynamical Systems and Control: A Lyapunovbased Appr, p.38, 2008.

[. Halbwachs, P. Caspi, P. Raymond, and D. Pilaud, The synchronous data flow programming language LUSTRE, Proceedings of the IEEE, vol.79, issue.9, pp.1305-1320, 1991.
DOI : 10.1109/5.97300

[. Halbwachs, F. Lagnier, and P. Raymond, Synchronous Observers and the Verification of Reactive Systems, Workshops in Computing, vol.isbn, pp.83-96, 1993.
DOI : 10.1007/978-1-4471-3227-1_8

[. Henrion and M. Korda, Convex Computation of the Region of Attraction of Polynomial Control Systems, IEEE Transactions on Automatic Control, vol.59, issue.2, pp.297-312, 2014.
DOI : 10.1109/TAC.2013.2283095
URL : https://hal.archives-ouvertes.fr/hal-00723019

[. Henrion, J. Lasserre, and C. Savorgnan, Approximate Volume and Integration for Basic Semialgebraic Sets, SIAM Review, vol.51, issue.4, pp.722-743, 2009.
DOI : 10.1137/080730287
URL : https://hal.archives-ouvertes.fr/hal-00297384

[. Herencia-zapana, R. Jobredeaux, S. Owre, P. Garoche, É. Féron et al., PVS Linear Algebra Libraries for Verification of Control Software Algorithms in C/ACSL, Proceedings, pp.147-161, 2012.
DOI : 10.1007/978-3-642-28891-3_15

N. J. Higham, Accuracy and Stability of Numerical Algorithms, pp.898713552-90, 1996.
DOI : 10.1137/1.9780898718027

C. A. Hoa69 and . Hoare, An axiomatic basis for computer programming, In: Commun. ACM, vol.12, issue.10, pp.576-580, 1969.

S. Dododzhanovich-ikramov and N. V. Savel-'eva, Conditionally definite matrices, In: Journal of Mathematical Sciences, vol.981, pp.2355379-2355422, 2000.

A. Ioualalen and M. Martel, Synthesizing accurate floating-point formulas, 2013 IEEE 24th International Conference on Application-Specific Systems, Architectures and Processors, pp.113-116, 2013.
DOI : 10.1109/ASAP.2013.6567563
URL : https://hal.archives-ouvertes.fr/hal-00835736

B. Jeannet and A. Miné, Apron: A Library of Numerical Abstract Domains for Static Analysis, pp.661-667978, 2009.
DOI : 10.1007/978-3-642-02658-4_52
URL : https://hal.archives-ouvertes.fr/hal-00786354

J. Luis-jerez, P. J. Goulart, S. Richter, G. A. Constantinides, E. C. Kerrigan et al., Embedded Online Optimization for Model Predictive Control at Megahertz Rates, IEEE Trans. Automat. Contr, vol.5912, issue.127, pp.3238-3251, 2014.

T. Kahsai, Y. Ge, and C. Tinelli, Instantiation-Based Invariant Discovery, pp.192-206, 2011.
DOI : 10.1007/3-540-45319-9_9

T. Kahsai, X. Thirioux, and P. Garoche, Hierarchical state machines as modular Horn clauses, Proceedings of the Second Workshop on Horn Clauses for Verification and Synthesis, p.113, 2016.

T. Kahsai and C. Tinelli, PKind: A parallel k-induction based model checker, Proceedings 10th International Workshop on Parallel and Distributed Methods in verifiCation, pp.55-62, 2011.
DOI : 10.4204/EPTCS.72.6

[. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica, vol.244, issue.S, pp.373-395, 1984.
DOI : 10.1007/BF02579150

D. Egor-george-karpenkov, P. Monniaux, and . Wendler, Program Analysis with Local Policy Iteration, Model Checking, and Abstract Interpretation -17th International Conference Proceedings, pp.127-146978, 2016.
DOI : 10.1007/978-3-662-49122-5_6

M. Karr, Affine relationships among variables of a program, Acta Informatica, vol.6, issue.2, pp.133-151, 1976.
DOI : 10.1007/BF00268497

[. Kojima, S. Shindoh, and S. Hara, Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices, SIAM Journal on Optimization, vol.7, issue.1, pp.86-125, 1997.
DOI : 10.1137/S1052623494269035

V. Ilya, E. Kolmanovsky, S. D. Garone, and . Cairano, Reference and command governors: A tutorial on their theory and automotive applications, 2014 American Control Conference, pp.226-241, 2014.

[. Komuravelli, A. Gurfinkel, and S. Chaki, SMT-Based Model Checking for Recursive Programs, Computer Aided Verification -26th International Conference, CAV 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, pp.17-34978, 2014.
DOI : 10.1007/978-3-319-08867-9_2

[. Komuravelli, A. Gurfinkel, S. Chaki, and E. M. Clarke, Automatic Abstraction in SMT-Based Unbounded Software Model Checking, Computer Aided Verification -25th International Conference, CAV 2013, pp.846-862978, 2013.
DOI : 10.1007/978-3-642-39799-8_59

[. Kong, S. Gao, W. Chen, and E. M. Clarke, dReach: ??-Reachability Analysis for Hybrid Systems, Tools and Algorithms for the Construction and Analysis of Systems -21st International Conference, TACAS 2015 Proceedings. Ed. by Christel Baier and Cesare Tinelli, pp.200-205978, 2015.
DOI : 10.1007/978-3-662-46681-0_15

M. Korda, D. Henrion, and C. N. Jones, Convex computation of the maximum controlled invariant set for discrete-time polynomial control systems, 52nd IEEE Conference on Decision and Control, pp.7107-7112, 2013.
DOI : 10.1109/CDC.2013.6761016

M. Korda, D. Henrion, and C. N. Jones, Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems, SIAM Journal on Control and Optimization, vol.52, issue.5, p.121, 2013.
DOI : 10.1137/130914565
URL : https://hal.archives-ouvertes.fr/hal-00804816

M. Korda, D. Henrion, and C. N. Jones, Inner approximations of the region of attraction for polynomial dynamical systems, IFAC Proceedings Volumes, vol.46, issue.23, p.121, 2012.
DOI : 10.3182/20130904-3-FR-2041.00002
URL : https://hal.archives-ouvertes.fr/hal-00740798

J. Lasserre, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802

J. Lasserre, Moments, Positive Polynomials and Their Applications Imperial College Press optimization series, p.34, 2009.

J. Lasserre, Tractable approximations of sets defined with quantifiers, Mathematical Programming, vol.17, issue.2, pp.507-527, 2015.
DOI : 10.1007/s10107-014-0838-1

J. Lee and G. E. Dullerud, Joint synthesis of switching and feedback for linear systems in discrete time, Proceedings of the 14th international conference on Hybrid systems: computation and control, HSCC '11, p.49, 2011.
DOI : 10.1145/1967701.1967731

J. Lee and G. E. Dullerud, Uniformly Stabilizing Sets of Switching Sequences for Switched Linear Systems, IEEE Transactions on Automatic Control, vol.52, issue.5, p.49, 2007.
DOI : 10.1109/TAC.2007.895924

J. Lee, E. Geir, . Dullerud, P. Pramod, and . Khargonekar, An output regulation problem for switched linear systems in discrete time, 2007 46th IEEE Conference on Decision and Control, pp.4993-4998, 2007.
DOI : 10.1109/CDC.2007.4434817

W. S. Levine, The control handbook. The electrical engineering handbook series Boca Raton (Fl, p.19, 1996.

J. Löfberg, YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), p.34, 2004.
DOI : 10.1109/CACSD.2004.1393890

W. Lohmiller, J. , and E. Slotine, On Contraction Analysis for Non-linear Systems, Automatica, vol.34, issue.6, pp.683-696, 1998.
DOI : 10.1016/S0005-1098(98)00019-3

D. Victor-magron, J. Henrion, and . Lasserre, Semidefinite Approximations of Projections and Polynomial Images of SemiAlgebraic Sets, In: SIAM Journal on Optimization, vol.254, p.121, 2015.

M. Martel, An Overview of Semantics for the Validation of Numerical Programs, 6th International Conference, VMCAI 2005, 2005.
DOI : 10.1007/978-3-540-30579-8_4

. Springer, isbn: 3-540-24297-X. doi: 10 . 1007 / 978 -3 -540 -30579 -8 _ 4, pp.59-77978, 2005.

D. [. Martin and . Jacobson, Copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints, Linear Algebra and its Applications, vol.35, pp.227-2580024379581902767, 1981.
DOI : 10.1016/0024-3795(81)90276-7

L. Kent-mcgovern, Computational Analysis of Real-Time Convex Optimization for Control Systems, p.127, 2000.

L. Kent-mcgovern and É. Féron, Requirements and hard computational bounds for realtime optimization in safety-critical control systems, Proceedings of the 37th IEEE Conference on, pp.3366-3371, 1998.

A. Megretski and A. Rantzer, System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, vol.42, issue.6, pp.819-830, 1997.
DOI : 10.1109/9.587335

A. Megretski and A. Rantzer, System Analysis via Integral Quadratic Constraints ? Part I, p.72, 1995.

[. Messine and A. Touhami, A General Reliable Quadratic Form: An Extension of Affine Arithmetic, Reliable Computing, vol.4, issue.3, pp.171-192, 2006.
DOI : 10.1007/s11155-006-7217-4

[. Mignone, G. Ferrari-trecate, and M. Morari, Stability and stabilization of piecewise affine and hybrid systems: an LMI approach, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.504-509, 2000.
DOI : 10.1109/CDC.2000.912814

A. Miné, The octagon abstract domain In: Higher-Order and Symbolic Computation 19, pp.31-100, 2006.

A. Miné, Weakly relational numerical abstract domains, pp.322-336, 2004.

E. Möhlmann and O. E. Theel, Stabhyli, Proceedings of the 16th international conference on Hybrid systems: computation and control, HSCC '13, pp.107-1122461347, 2013.
DOI : 10.1145/2461328.2461347

D. Monniaux, Applying the Z-transform for the static analysis of floating-point numerical filters In: CoRR abs/0706, pp.2520252-56, 2007.

D. Monniaux, The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, p.89, 2008.
DOI : 10.1145/1353445.1353446
URL : https://hal.archives-ouvertes.fr/hal-00128124

D. Monniaux and P. Corbineau, On the Generation of Positivstellensatz Witnesses in Degenerate Cases, Second International Conference Proceedings, pp.249-264978, 2011.
DOI : 10.1137/1038003
URL : https://hal.archives-ouvertes.fr/hal-00594761

D. Monniaux and P. Schrammel, Speeding Up Logico-Numerical Strategy Iteration, Proceedings. Ed. by, pp.253-267978, 2014.
DOI : 10.1007/978-3-319-10936-7_16

R. D. Monteiro, Primal--Dual Path-Following Algorithms for Semidefinite Programming, SIAM Journal on Optimization, vol.7, issue.3, pp.663-678, 1997.
DOI : 10.1137/S1052623495293056

T. Samuel-motzkin, Two consequences of the transposition theorem on linear inequalities, In: Econometrica, vol.192, pp.184-185, 1951.

L. Mendonça-de-moura and N. Bjørner, Z3: An Efficient SMT Solver, Lecture Notes in Computer Science, vol.4963, issue.113, pp.337-340, 2008.
DOI : 10.1007/978-3-540-78800-3_24

Y. Moy, Sufficient Preconditions for Modular Assertion Checking, 9th International Conference Proceedings, pp.188-202978, 2008.
DOI : 10.1007/978-3-540-78163-9_18

M. Müller-olm and H. Seidl, Polynomial Constants Are Decidable, 9th International Symposium Proceedings, pp.3-540, 2002.
DOI : 10.1007/3-540-45789-5_4

Y. Nesterov and A. Nemirovski, A general approach to the design of optimal methods for smooth convex functions minimization, In: Ekonomika i Matem. Metody, vol.24, pp.509-517, 1988.

Y. Nesterov and A. Nemirovski, Interior-point Polynomial Algorithms in Convex Programming
DOI : 10.1137/1.9781611970791

Y. Nesterov and A. Nemirovski, Self-Concordant functions and polynomial time methods in convex programming, Materialy po matematicheskomu obespecheniiu EVM. USSR Academy of Sciences, Central Economic & Mathematic Institute, p.103, 1989.

T. Tuan, M. Nguyen, V. Lazar, and . Spinu, Interpolation of polytopic control Lyapunov functions for discrete-time linear systems In: {IFAC} Proceedings Volumes 47, 19th {IFAC} World Congress, pp.2297-2302, 2014.

J. Nocedal and S. J. Wright, Numerical Optimization. 2nd, p.32, 2006.

[. Norris and M. Wagner, Airbus A380: Superjumbo of the 21st Century, 2005.

W. Peter, J. C. O-'hearn, H. Reynolds, and . Yang, Local Reasoning about Programs that Alter Data Structures, 15th International Workshop, CSL 2001. 10th Annual Conference of the EACSL, pp.3-540, 2001.

M. Oulamara and A. J. Venet, Abstract Interpretation with Higher-Dimensional Ellipsoids and Conic Extrapolation, Computer Aided Verification -27th International Conference, CAV 2015, pp.415-430978, 2015.
DOI : 10.1007/978-3-319-21690-4_24
URL : https://hal.archives-ouvertes.fr/hal-01202346

S. Owre and N. Shankar, Theory Interpretation in PVS, Tech. rep. SRI International, p.83, 2001.

[. Pakmehr, T. Wang, R. Jobredeaux, M. Vivies, and É. Féron, Verifiable Control System Development for Gas Turbine Engines, p.78, 1311.

P. A. Parrilo, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.10107-10110, 2003.
DOI : 10.1007/s10107-003-0387-5

M. Péron and N. Halbwachs, An Abstract Domain Extending Difference-Bound Matrices with Disequality Constraints, Model Checking, and Abstract Interpretation, 8th International Conference Proceedings, pp.268-282978, 2007.
DOI : 10.1007/978-3-540-69738-1_20

A. Podelski and S. Wagner, Region Stability Proofs for Hybrid Systems, 5th International Conference Proceedings, pp.320-335978, 2007.
DOI : 10.1007/978-3-540-75454-1_23

[. Prabhakar and M. G. Soto, Abstraction Based Model-Checking of Stability of Hybrid Systems, Computer Aided Verification -25th International Conference, CAV 2013, Saint Petersburg, Russia, pp.280-295978, 2013.
DOI : 10.1007/978-3-642-39799-8_20

A. Rantzer, On the Kalman???Yakubovich???Popov lemma, Systems & Control Letters, vol.28, issue.1, pp.167-691100063, 1996.
DOI : 10.1016/0167-6911(95)00063-1

A. Rantzer, On the Kalman-Yakubovich-Popov Lemma for Positive Systems

S. Ratschan and Z. She, Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4377-4394090749955, 2010.
DOI : 10.1137/090749955

S. Richter, C. N. Jones, and M. Morari, Certification aspects of the fast gradient method for solving the dual of parametric convex programs, Mathematical Methods of Operations Research, vol.57, issue.6, pp.305-321, 2013.
DOI : 10.1007/s00186-012-0420-7

P. Roux, Formal Proofs of Rounding Error Bounds, Journal of Automated Reasoning, vol.35, issue.2, pp.10817-10832, 2015.
DOI : 10.1007/s10817-015-9339-z
URL : https://hal.archives-ouvertes.fr/hal-01091189

P. Roux, Static Analysis of Control Command Systems: Synthetizing Non-Linear Invariants, pp.2013-92

P. Roux and P. Garoche, Integrating Policy Iterations in Abstract Interpreters, 11th International Symposium, ATVA 2013, pp.240-254978, 2013.
DOI : 10.1007/978-3-319-02444-8_18

P. Roux, R. Jobredeaux, P. Garoche, and É. Féron, A generic ellipsoid abstract domain for linear time invariant systems, Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control, HSCC '12, pp.105-1142185651, 2012.
DOI : 10.1145/2185632.2185651
URL : https://hal.archives-ouvertes.fr/hal-00608673

C. Special and . Rtca, DO-178C, Software Considerations in Airborne Systems and Equipment Certification, p.3, 2011.

S. M. Rump, Verification methods, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, 2010.
DOI : 10.1145/1837934.1837937

S. M. Rump, Verification of Positive Definiteness, BIT Numerical Mathematics, vol.46, issue.2, pp.433-452, 2006.
DOI : 10.1007/s10543-006-0056-1

J. Rushby, The Versatile Synchronous Observer, pp.978-981, 2012.
DOI : 10.1007/978-3-642-33296-8_1

[. Sankaranarayanan, H. Sipma, and Z. Manna, Non-linear loop invariant generation using Gröbner bases, Proceedings of the 31st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp.318-329964028, 2004.

[. Sankaranarayanan and A. Tiwari, Relational Abstractions for Continuous and Hybrid Systems, Computer Aided Verification -23rd International Conference, pp.686-702978, 2011.
DOI : 10.1007/s10703-007-0044-3

Y. Seladji and O. Bouissou, Numerical Abstract Domain Using Support Functions, In: NFM, pp.2013-56
DOI : 10.1007/978-3-642-38088-4_11

M. Sheeran, S. Singh, G. Stålmarck, :. Fmcad, . Ed et al., Checking Safety Properties Using Induction and a SAT-Solver, LNCS. Springer, vol.1954, issue.49, pp.3-540, 2000.
DOI : 10.1007/3-540-40922-X_8

S. Srivastava and S. Gulwani, Program verification using templates over predicate abstraction, ACM SIGPLAN Notices, vol.44, issue.6, pp.223-234, 2009.
DOI : 10.1145/1543135.1542501

J. Stolfi and L. Henrique-de-figueiredo, Self-Validated Numerical Methods and Applications. Brazilian Mathematics Colloquium monograph, p.99, 1997.

A. M. Turing, Checking a large routine In: Report of a Conference on High Speed Automatic Calculating Machines, 1949.

. Vb96-]-lieven, S. Vandenberghe, and . Boyd, Semidefinite Programming, In: SIAM Review, vol.381, pp.49-95, 1996.

A. Stephen and . Vavasis, Quadratic programming is in NP, In: Information Processing Letters, vol.36, issue.2, pp.73-77002001909090100, 1990.

G. Vinnicombe, Uncertainty and Feedback: H [infinity] Loop-shaping and the [nu]-gap Metric, World Scientific, p.74, 2001.
DOI : 10.1142/p140

T. Wang, Credible Autocoding of Control Software, pp.2015-82

[. Wang, R. Jobredeaux, H. Herencia-zapana, P. Garoche, A. Dieumegard et al., From Design to Implementation: An Automated, Credible Autocoding Chain for Control Systems In: Advances in Control System Technology for Aerospace Applications Lecture Notes in Control and Information Sciences, Ed. by Éric Féron, vol.460, issue.82, pp.978-981

T. Wang, R. Jobredeaux, M. Pantel, and P. Garoche, Éric Féron, and Didier Henrion Credible Autocoding of Convex Optimization Algorithms, In: Optimization and Engineering, 2016.

C. Jan and . Willems, Dissipative dynamical systems part I: General theory In: Archive for rational mechanics and analysis 45, pp.321-351, 1972.

A. Vladimir and . Yakubovich, S-procedure in nonlinear control theory, In: Vestnik Leningrad University, vol.1, pp.62-77, 1971.

A. Vladimir and . Yakubovich, The solution of certain matrix inequalities in automatic control theory, In: Soviet Math. Dokl, vol.3, pp.620-623, 1962.

M. Yamashita, K. Fujisawa, K. Nakata, M. Nakata, M. Fukuda et al., A high-performance software package for semidefinite programs : SDPA7, Dept. of Information Sciences, p.33, 2010.

Q. Yang, Minimum Decay Rate of a Family of Dynamical Systems, pp.40-71, 1992.