.. Détectabilité-de-défaut-au-niveau-du-sous-système-actionneur, 108 3.2. Inversibilité du sous-système procédé, p.109

.. Approche-basée-sur-les-observateurs-par-intervalles, 110 4.1.1. Description de l'approche pour l'isolation de défauts actionneurs, p.110

.. Filtre-de-paramètre, 110 b) Filtre de défaut, p.114

.. Présentation-des-méthodes-de-diagnostic, 18 a) Approches quantitatives

M. Méthodes-avec, 23 a) Approches qualitatives, p.25

.. Etude-des-systèmes-linéaires, 34 2.1.1. Equations d'état d'un système linéaire 35 a), 34 2.1.2. Propriétés des systèmes linéaires 36 c) Stabilisabilité et, p.37

.. Etude-des-systèmes-non-linéaires and .. Observabilité-faible, 38 2.2.1. Equations d'état d'un système non linéaire 39 a) Indistinguabilité (indiscernabilité) 39 b), 38 2.2.2. Propriétés des systèmes non linéaires, p.40

.. Modèle-d-'un-procédé-de-traitement-des-eaux-usées, 61 2.1. Description d'une station d'épuration des eaux usées, p.61

.. Rapide-historique:-la-pile-de-fermi, 83 3.2 Histoire de la physique nucléaire 84 3.3. Description d'un réacteur nucléaire, p.86

.. Détectabilité-de-défaut-au-niveau-du-sous-système-actionneur, 108 3.2. Inversibilité du sous-système procédé, p.109

.. Approche-basée-sur-les-observateurs-par-intervalles, 110 4.1.1. Description de l'approche pour l'isolation de défauts actionneurs, p.110

.. Filtre-de-paramètre, 110 b) Filtre de défaut, p.114

K. Adjallah, D. Maquin, and J. Ragot, Non-linear observer-based fault detection, Proceedings of IEEE International Conference on Control and Applications CCA-94, pp.1115-1120, 1994.
DOI : 10.1109/CCA.1994.381359
URL : https://hal.archives-ouvertes.fr/hal-00201420

X. Aiping, Observateurs adaptatifs non-linéaires et diagnostic de pannes, Thèse de l'Université de Rennes 1, 2002.

A. Akhenak, M. Chadli, J. Ragot, and D. Et-maquin, Estimation of state and unknown inputs of a nonlinear system represented by a multiple model, The 11th IFAC Symposium on Automation in Mineral and Metal processing, 2004.

K. J. Astrom, P. Albertos, M. Blanke, A. Isidori, R. Santz et al., Control of complex systems, 2000.

J. August, Applied reliability-centered maintenance, 2000.

M. Basseville and I. Nikiforov, Statistical change detection, 1994.
URL : https://hal.archives-ouvertes.fr/hal-01151830

M. Basseville, Model-based statistical signal processing and decision theoretical approach to monitoring, Proc. IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, pp.1-12, 2003.

G. Bastin and M. R. Gevers, Stable adaptive observers for nonlinear time-varying systems, IEEE Transactions on Automatic Control, vol.33, issue.7, pp.650-658, 1988.
DOI : 10.1109/9.1273

R. V. Beard, Failure accommodation in linear systems through self reorganization, 1971.

H. Blom and E. Bloem, Particle filtering for stochastic hybrid systems, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004.
DOI : 10.1109/CDC.2004.1428969

G. Bornard, F. Celle-couenne, and G. Gilles, Observabilité et observateurs sur les systèmes non linéaires T.1, Modélisation-Estimation, pp.177-221, 1993.

M. Boutayeb and M. Et-darouach, Observers design for linear time-varying systems, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.3183-3187, 2000.
DOI : 10.1109/CDC.2000.912188

B. Carlsson, M. Salgodo, and G. C. Goodwin, A new method for fault detection and diagnosis, 1988.

P. T. Chee and C. Edwards, Sliding mode observers for reconstruction of simultaneous actuator and sensor faults, Proceedings of the 42nd Conference on Decision and Control CDD'03, 2003.

J. Chen and R. J. Patton, Robust model-based fault diagnosis for dynamic systems, 1999.
DOI : 10.1007/978-1-4615-5149-2

J. Chen and M. B. Beck, Modeling, control and on-line estimation of activated sludge bulking, Wat. Sci. Tech, vol.28, pp.11-12, 1993.

W. Chen and M. Saif, An actuator fault isolation strategy for linear and nonlinear systems, Proceedings of the American Control Conference ACC'05, 2005.

E. Y. Chow and A. S. Willsky, Analytical redundancy and the design of robust failure detection systems, IEEE Transactions on Automatic Control, vol.29, issue.7, pp.603-614, 1984.
DOI : 10.1109/TAC.1984.1103593

J. Colomer and J. Meléndez, A family of FIR differentiators based on a polynomial least squares estimation, Proc. Of the European Control Conference, pp.2802-2807, 2001.

D. Cox, J. Little, O. Shea, and D. , Ideals, varieties, and algorithms, pp.47-166, 1996.

P. Dague, Diagnostic, intelligence artificielle et reconnaissance des formes, Traité IC2 Productique, Editions Hermes, Chapitre 1: Théorie logique du diagnostic à base de modèles, pp.17-105, 2001.

S. Dennis, M. Bernstein, and . Mathematic, Theory, Facts, and Formulas with Application to Linear Systems Theory, 2005.

T. Denoeux, Diagnostic par reconnaissance de formes : approches non probabilistes, pp.143-178, 2001.

F. Deza, E. Busvelle, J. P. Gauthier, and D. Rakotopara, High gain estimation for nonlinear systems, Systems & Control Letters, vol.18, issue.4, pp.313-322, 1990.
DOI : 10.1016/0167-6911(92)90059-2

S. Diop, Elimination in control theory Mathematics of control, signals, and systems, pp.17-32, 1991.

D. Dochain, State and parameter estimation in chemical and biochemical processes: a tutorial, Journal of Process Control, vol.13, issue.8, pp.801-810, 2003.
DOI : 10.1016/S0959-1524(03)00026-X

P. L. Dold, G. A. Ekama, and G. V. Marais, A GENERAL MODEL FOR THE ACTIVATED SLUDGE PROCESS, Progress in Water Technology, pp.47-77, 1980.
DOI : 10.1016/B978-1-4832-8438-5.50010-8

D. Eduardo and . Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Series: Textbooks in Applied Mathematics, 1998.

C. Edwards, S. K. Spurgeon, and R. J. Patton, Sliding mode observers for fault detection and isolation, Automatica, vol.36, issue.4, pp.541-553, 2000.
DOI : 10.1016/S0005-1098(99)00177-6

E. Etien, Caractérisation des systèmes à représentation continue par les moments fréquentiels : Application à l'identification et à la réduction de modèle, Thèse de doctorat. École Supérieure d'Ingénieurs de Poitiers, 1997.

I. Fagarasan, S. Ploix, and S. Gentil, Causal fault detection and isolation based on a set-membership approach, Automatica, vol.40, pp.2099-2110, 2004.

D. Fragkoulis, G. Roux, and B. Dahhou, A new scheme for detection, isolation and identification of single and multiple actuator faults, International Conference on Prognostic and Health Management, 2007.

D. Fragkoulis, Détection et localisation des défauts provenant des actionneurs et des capteurs : application sur un système non linéaire, 2008.

P. M. Frank, Advances in observer-based fault diagnosis in dynamic systems, Engineering Simulation, vol.13, pp.717-760, 1996.

P. M. Frank, Analytical and Qualitative Model-based Fault Diagnosis ??? A Survey and Some New Results, European Journal of Control, vol.2, issue.1, pp.6-28, 1996.
DOI : 10.1016/S0947-3580(96)70024-9

P. M. Frank, Enhancement of robustness in observer-based fault detection???, International Journal of Control, vol.4, issue.4, pp.955-981, 1994.
DOI : 10.1016/0005-1098(76)90041-8

P. M. Frank and S. Ding, Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of Process Control, vol.7, issue.6, pp.403-424, 1997.
DOI : 10.1016/S0959-1524(97)00016-4

E. A. Garcia and P. M. Frank, Deterministic nonlinear observer-based approaches to fault diagnosis: A survey, Control Engineering Practice, vol.5, issue.5, pp.663-670, 1997.
DOI : 10.1016/S0967-0661(97)00048-8

J. P. Gauthier, H. Hammouri, and S. Othman, A simple observer for nonlinear systems applications to bioreactors, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.875-880, 1992.
DOI : 10.1109/9.256352

J. P. Gauthier and G. Bornard, Observability for any<tex>u(t)</tex>of a class of nonlinear systems, IEEE Transactions on Automatic Control, vol.26, issue.4, pp.922-926, 1981.
DOI : 10.1109/TAC.1981.1102743

J. Gertler, Fault detection and isolation using parity relations, Control Engineering Practice, vol.5, issue.5, pp.653-661, 1997.
DOI : 10.1016/S0967-0661(97)00047-6

J. Gertler, Fault detection and diagnosis in engineering systems, 1998.

J. L. Gouzé, A. Rapaport, and M. Z. Hadj-sadok, Interval observers for uncertain biological systems, Ecological Modelling, vol.133, issue.1-2, pp.45-56, 2000.
DOI : 10.1016/S0304-3800(00)00279-9

Y. Grandvalet, M. Masson, and . Chapitre, Réseaux de neurones pour le diagnostic, Traité IC2, Diagnostic : Intelligence Artificielle et Reconnaissance des Formes, pp.179-218, 2001.

W. Gujer, M. Henze, T. Mino, and M. C. Van-loosdrecht, Activated Sludge Model No. 3, Water Science and Technology, vol.39, issue.1, pp.183-193, 1999.
DOI : 10.1016/S0273-1223(98)00785-9

H. Hammouri, M. Kinnaert, E. Yaagoubi, and E. H. , Observer-based approach to fault detection and isolation for nonlinear systems, IEEE Transactions on Automatic Control, vol.44, issue.10, pp.1879-1884, 1999.
DOI : 10.1109/9.793728

M. Henze, W. Gujer, T. Mino, and M. C. Van-loosdrecht, Activated Sludge Models ASM1, ASM2, ASM2d and ASM3, Water Intelligence Online, vol.5, issue.0, 2000.
DOI : 10.2166/9781780402369

M. Henze, C. P. Leslie-grady, W. Gujer, G. V. Maris, and T. Matsuo, Activated sludge process model No, 1987.

R. Hermann and A. J. Et-kerner, Nonlinear controllability and observability, IEEE Transactions on Automatic Control, vol.22, issue.5, pp.728-740, 1977.
DOI : 10.1109/TAC.1977.1101601

S. Ibrir, Online exact differentiation and notion of asymptotic algebraic observers, IEEE Transactions on Automatic Control, vol.48, issue.11, pp.2055-2060, 2003.
DOI : 10.1109/TAC.2003.819303

R. Isermann, Process fault detection based on modeling and estimation methods???A survey, Automatica, vol.20, issue.4, pp.387-404, 1984.
DOI : 10.1016/0005-1098(84)90098-0

R. Isermann, Supervision, fault-detection and fault-diagnosis methods ??? An introduction, Control Engineering Practice, vol.5, issue.5, pp.639-652, 1997.
DOI : 10.1016/S0967-0661(97)00046-4

R. Isermann and P. Ballé, Trends in the application of model-based fault detection and diagnosis of technical processes, Control Engineering Practice, vol.5, issue.5, pp.709-719, 1997.
DOI : 10.1016/S0967-0661(97)00053-1

R. Isermann, R. Schwarz, and S. Stolzl, Fault-tolerant drive-by-wire systems, IEEE Control Systems Magazine, vol.22, issue.5, pp.64-81, 2002.
DOI : 10.1109/MCS.2002.1035218

U. Jeppsson, Modeling aspects of wastewater treatment processes, 1996.

I. Jolliffe, Princpal Component Analysis, 1986.

H. L. Jones, Failure detection in linear systems, Ph.D. dissertation, Dep. Aeronautics and Astronautics, Mass. Inst. Technol, 1973.

S. Julien, Modélisation et estimation pour le contrôle d'un procédé boues activées éliminant l'azote des eaux résiduaires urbaines, 1997.

K. Roy, R. N. Banavar, and S. Thangasamy, Application of fault detection and identification (FDI) techniques in power regulating systems of nuclear reactors, IEEE Transactions on Nuclear Science, vol.45, issue.6, 1998.
DOI : 10.1109/23.736198

R. E. Kalman, On the general theory of control systems, first IFAC World Congress, 1960.
DOI : 10.1109/TAC.1959.1104873

R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961.
DOI : 10.1115/1.3658902

S. M. Kay, Modern Spectral Estimation: Theory and Application, 1988.

M. Kinnaert, Robust fault detection based on observers for bilinear systems, Automatica, vol.35, issue.11, pp.1829-1842, 1999.
DOI : 10.1016/S0005-1098(99)00067-9

N. Kiupel and P. M. Frank, A Fuzzy FDI decision making system for the support of the human operator, IFAC Safeprocess'97, pp.731-736, 1997.

B. Koppen-seliger and P. M. Frank, Neural network in model-based fault Diagnosis, 13 th IFAC World Congress, pp.67-72, 1996.

G. Kreisselmeier, Adaptive observers with exponential rate of convergence, IEEE Transactions on Automatic Control, vol.22, issue.1, pp.2-8, 1977.
DOI : 10.1109/TAC.1977.1101401

V. Krishmaswami, C. Siviero, F. Cabognani, and V. Utkin, Application of sliding mode observers to automobile power-train, Proc. of the IEEE int. Conf. On Cont. Appli, p.355, 1996.

B. Larroque, Observateurs de systèmes linéaires Application à la détection et localisation de fautes, thèse de doctorat, l'équipe de Production, 2008.

Z. Li and B. Dahhou, Parameter intervals used for fault isolation in non-linear dynamic systems, International Journal of Modelling, Identification and Control, vol.1, issue.3, pp.215-229, 2006.
DOI : 10.1504/IJMIC.2006.011945

Z. Li and B. Dahhou, Fault isolation for nonlinear dynamic systems based on parameter intervals, International Journal of Systems Science, vol.37, issue.7, pp.531-547, 2007.
DOI : 10.1002/1099-1115(200011)14:7<759::AID-ACS620>3.0.CO;2-Y

Z. Li, Contribution à l'élaboration d'algorithmes d'isolation et d'identification de défauts dans les systèmes non linéaires, Thèse de l'Institut National des Sciences Appliquées de Toulouse, 2006.

G. Luders and K. S. Narendra, A new canonical form for an adaptive observer, IEEE Transactions on Automatic Control, vol.19, issue.2, pp.117-119, 1974.
DOI : 10.1109/TAC.1974.1100499

G. Luders and K. S. Narendra, An adaptive observer and identifier for a linear system, IEEE Transactions on Automatic Control, vol.18, issue.5, pp.196-499, 1973.
DOI : 10.1109/TAC.1973.1100369

D. G. Luenberger, Observers for multivariable systems, IEEE Transactions on Automatic Control, vol.11, issue.2, pp.190-197, 1966.
DOI : 10.1109/TAC.1966.1098323

D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971.
DOI : 10.1109/TAC.1971.1099826

J. Lunze, Diagnosis of quantized systems, 4 th IFAC Symposium on Fault Detection. Supervision and Safety for Technical Processes (SAFEPROCESS-2000, pp.28-39, 2000.

S. Methnani, Diagnostic, reconstruction et identification des défauts capteurs et actionneurs: application aux stations d'épurations des eaux usées, 2012.

M. A. Massoumnia, A geometric approach to failure detection and identification in linear systems, Dep. Aeronautics and Astronautics, Mass. Inst. Technol, 1986.

M. Massoumnia, A geometric approach to the synthesis of failure detection filters, IEEE Transactions on Automatic Control, vol.31, issue.9, pp.839-846, 1986.
DOI : 10.1109/TAC.1986.1104419

D. Q. Mayne and H. Michalska, Moving horizon observer-based control, [1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992.
DOI : 10.1109/CDC.1992.371162

R. K. Mehra and L. Peshon, An innovative approach to fault detection and diagnosis systems, Automatica, vol.7, pp.737-640, 1971.

K. S. Michael and L. M. James, Invertibility of linear time-invariant dynamical systems, IEEE Transactions on automatic control, vol.14, issue.2, 1969.

E. Morel, B. Tartakovsky, R. Guiot, and M. Perrier, Design of a multi-model observer-based estimator for anaerobic reactor monitoring, Computers & Chemical Engineering, vol.31, issue.2, pp.78-85, 2006.
DOI : 10.1016/j.compchemeng.2006.05.003

F. Nejjari, Benchmark of an activated sludge plant, Internal report, 2001.

H. Nijmeijer and T. I. Fossen, New Directions in nonlinear observer design, 1999.
DOI : 10.1007/BFb0109917

J. Park and G. Rizzoni, A new interpretation of the fault detection filter Part 1: Closed-form algorithm, International Journal of Control, vol.62, issue.5, pp.767-787, 1994.
DOI : 10.1109/TAC.1987.1104682

J. Park and G. Rizzoni, A new interpretation of the fault detection filter: part2, International Journal of Control, vol.60, pp.1033-1055, 1994.

R. J. Patton and J. Chen, A REVIEW OF PARITY SPACE APPROACHES TO FAULT DIAGNOSIS, Proceedings of the 1st IFAC/IMACS Symposium on Fault Detection, Supervision and Safety of Technical Processes, 1991.
DOI : 10.1016/B978-0-08-041275-7.50012-0

R. J. Patton, Fault detection and diagnosis in Aerospace systems using analytical redundancy, computing and control engineering journal, pp.127-136, 1991.

L. Qing, observer based fault detection for nuclear reactor, 2011.

S. Raghavan and K. Et-hedrick, Observer design for a class of nonlinear systems, International Journal of Control, vol.59, issue.2, pp.515-528, 1994.
DOI : 10.1109/9.53535

R. Rajamani, Observers for Lipschitz nonlinear systems, IEEE Transactions on Automatic Control, vol.43, issue.3, pp.397-401, 1998.
DOI : 10.1109/9.661604

R. Reiter, A theory of diagnosis from first principles, Artificial Intelligence, vol.32, issue.1, pp.57-96, 1987.
DOI : 10.1016/0004-3702(87)90062-2

P. Reuss, Précis de neutronique, Collection Génie Atomique, 2003.

N. Revol, Introduction à l'arithmétique par intervalles, 2001.

F. Sallem, B. Dahhou, G. Roux, and A. Kamoun, Actuators faults detection and isolation for nonlinear systems based on adaptive observers, th international conference on Science and Techniques of Automatic control and computer engineering, p.2011, 2011.

F. Sallem, B. Dahhou, and A. Kamoun, A comparative analysis of two formulations for actuator faults detection and Isolation: application to a waste water treatment process, International Journal on Sciences and Techniques of Automatic control & computer engineering IJSTA, vol.7, issue.1, pp.1792-1816, 2013.

F. Sallem, B. Dahhou, . Z. Li, and . Kamoun, A, System inversion and actuator fault detection and isolation for linear systems: application to a nuclear reactor, 2013.

G. Schreier, J. Ragot, R. J. Patton, and . P. Frank, Observer design for a class of nonlinear systems, Proc. IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, pp.498-503, 1997.

D. Schroder, Intelligent Observer and Control Design for Nonlinear Systems, 2000.
DOI : 10.1007/978-3-662-04117-8

H. Sira-ramirez and S. K. Spurgeon, On the robust design of sliding observers for linear systems, Systems & Control Letters, vol.23, issue.1, pp.9-14, 1994.
DOI : 10.1016/0167-6911(94)90076-0

H. Sira-ramirez, On the sliding mode control of nonlinear systems, Systems & Control Letters, vol.19, issue.4, pp.303-312, 1992.
DOI : 10.1016/0167-6911(92)90069-5

J. J. Slotine and S. S. Sastry, Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators???, International Journal of Control, vol.22, issue.2, pp.465-492, 1983.
DOI : 10.1080/00207178308933088

J. J. Slotine, J. K. Hedrick, and E. A. Misawa, On Sliding Observers for Nonlinear Systems, Journal of Dynamic Systems, Measurement, and Control, vol.109, issue.3, 1987.
DOI : 10.1115/1.3143852

M. Staroswiecki and G. Comtet-varga, Analytical redundancy relations for fault detection and isolation in algebraic dynamic systems, Automatica, vol.37, issue.5, pp.687-699, 2001.
DOI : 10.1016/S0005-1098(01)00005-X

H. J. Sussmann, Single-input observability of continuous-time systems, Mathematical Systems Theory, vol.301, issue.6, pp.371-393, 1979.
DOI : 10.1007/BF01776584

F. Szigeti, Kalman's rank condition for infinite-dimensional time-dependent systems, Proc. Differentil Eq. Conference: equadiff'91, pp.927-931, 1991.

F. E. Thau, Observing the state of non-linear dynamic systems???, International Journal of Control, vol.82, issue.3, pp.471-479, 1973.
DOI : 10.1109/TAC.1966.1098323

M. W. Thein and E. Misawa, A Parallel Observer System for Multirate State Estimation, Proceedings of the American Control Conference ACC'99, 1999.

L. Travé-massuyès, P. Dague, and F. Guérrin, Le raisonnement qualitatif pour les sciences de l'ingénieur. Hermès, 1997.

J. Tsinias, Observer design for nonlinear systems, Systems & Control Letters, vol.13, issue.2, pp.135-142, 1989.
DOI : 10.1016/0167-6911(89)90030-3

G. Videau, Méthodes garanties pour l'estimation d'état et le contrôle de cohérence des systèmes non linéaires à temps continu, Thèse de doctorat des Sciences Physiques et de l'Ingénieur, 2009.

A. Villemeur, Sureté de fonctionnement des systèmes industriels, Fiabilité Facteurs humains Informatisation. Eyrolles, 1988.

H. Wang, Z. J. Huang, and S. Daley, On the use of adaptive updating rules for actuator and sensor fault diagnosis, Automatica, vol.33, issue.2, pp.33-217, 1997.
DOI : 10.1016/S0005-1098(96)00155-0

C. Wen and M. Saif, Robust fault detection in uncertain nonlinear systems via a second order sliding mode observer, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), pp.573-578, 2001.
DOI : 10.1109/CDC.2001.980164

J. E. White and J. L. Speyer, Detection filter design: Spectral theory and algorithms, IEEE Transactions on Automatic Control, vol.32, issue.7, pp.593-603, 1987.
DOI : 10.1109/TAC.1987.1104682

Y. Xing-gang and C. Edwards, Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems, Proceedings of the 44th IEEE Conference on Decision and Control, 2005.
DOI : 10.1109/CDC.2005.1582286

S. T. Yau and G. Q. Hu, Finite Dimensional Filters with Nonlinear Drift, XI, Advances in Mathematics, vol.140, issue.2, pp.142-148, 2001.
DOI : 10.1006/aima.1998.1767
URL : http://doi.org/10.1006/aima.1998.1767

M. Zeitz, The extended Luenberger observer for nonlinear systems, Systems & Control Letters, vol.9, issue.2, pp.149-156, 1987.
DOI : 10.1016/0167-6911(87)90021-1

Q. Zhang, Fault detection and isolation based on adaptive observers for nonlinear dynamic systems, Rapport technique 1261, 1999.

A. Zolghadri, An algorithm for real-time failure detection in Kalman filters, IEEE Transactions on Automatic Control, vol.41, issue.10, pp.41-1537, 1996.
DOI : 10.1109/9.539440