D. Gucik-derigny, R. Outbib, M. Ouladsinep2, ]. Gucik-derigny, R. Outbib et al., Prognosis applied to an electromechanical system, a nonlinear approach based on sliding mode observer Annual Conference on European Safety and Reliability Association, ESREL2011 , Troyes, France, septembre 2011Prognosis applied to an electromechanical system, a nonlinear approach based on high gain observerDiagnostic prédictif sous contrainte temporelle" . Conférence Internationale Francophone d'Automatique, CIFA 2010Estimation of Damage Behaviour for Model-Based-Prognosis, IEEE International Conference on Prognostics and Health Management 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical ProcessesPredictive diagnosis under temporal constraint applied to an electromechanical system : a comparative approach based on observers" . IEEE Transactions on Reliability, 2011.

R. [. Gucik-derigny and . Outbib, Prognosis of systems : concept, methodologies and application

R. [. Gucik-derigny, M. Outbib, and . Ouladsine, Pronostic des systèmes complexes à base d'observateurs non linéaires". Journées Nationales-MACS, juin 2011 Analytic prognostic model for a dynamic system, International Review of Automatic Control, vol.3, issue.6, pp.568-577, 2010.

E. Adams and M. Nataraju, A nonlinear dynamical systems framework for structural diagnosis and prognosis, International Journal of Engineering Science, vol.40, issue.17, pp.1919-1941, 2002.
DOI : 10.1016/S0020-7225(02)00112-X

A. Norme and A. , Terminologie de la maintenance, 2001.

M. Althoff, Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars, 2010.

M. Althoff, O. Stursberg, and M. Buss, Reachability analysis of linear systems with uncertain parameters and inputs, 2007 46th IEEE Conference on Decision and Control, pp.726-732, 2007.
DOI : 10.1109/CDC.2007.4434084

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, pp.4042-4048, 2008.
DOI : 10.1109/CDC.2008.4738704

M. Althoff, O. Stursberg, and M. Buss, Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear Analysis : Hybrid Systems, pp.233-249, 2010.

A. Asarin, T. Dang, G. Frehse, A. Girard, C. L. Guernic et al., Recent progress in continuous and hybrid reachability analysis, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, pp.1582-1587, 2006.
DOI : 10.1109/CACSD-CCA-ISIC.2006.4776877
URL : https://hal.archives-ouvertes.fr/hal-00307031

Y. Asiedu and P. Gu, Product life cycle cost analysis: State of the art review, International Journal of Production Research, vol.36, issue.4, pp.1366-588, 1998.
DOI : 10.1080/002075498193444

M. Azam, F. Tu, and K. G. Pattipati, Condition based predictive maintenance of industrial power systems, SPIE Conference on Fault Diagnosis, Prognosis and System Health Management, 2002.

W. Batko, Prediction method in technical diagnostics, Cracov Mining Academy, 1984.

M. Bengtsson, Standardization issues in condition based maintenance, Proceedings of the 16th International Congress on Condition Monitoring and Diagnostic Engineering Management, pp.1-10, 2003.

O. Bernard and J. L. Gouze, Closed loop observers bundle for uncertain biotechnological models, Journal of Process Control, vol.14, issue.7, pp.765-774, 2004.
DOI : 10.1016/j.jprocont.2003.12.006
URL : https://hal.archives-ouvertes.fr/inria-00071676

S. P. Bhat and D. S. Bernstein, Geometric homogeneity with applications to finite-time stability, Mathematics of Control, Signals, and Systems, vol.17, issue.2, pp.101-127, 2000.
DOI : 10.1007/s00498-005-0151-x

S. P. Bhat and D. S. Bernstein, Finite-Time Stability of Continuous Autonomous Systems, SIAM Journal on Control and Optimization, vol.38, issue.3, pp.751-766, 2005.
DOI : 10.1137/S0363012997321358

G. P. Box, G. M. Jenkins, and G. C. , Time series analysis forecasting and control, 1994.

C. Byington, M. Roemer, and T. Galie, Prognostic enhancements to diagnostic systems for improved condition-based maintenance, Proceedings of IEEE Aerospace Conference, 2002.

C. S. Byington, M. J. Roemer, and P. W. Kalgren, Verification and validation of diagnostic/prognostic algorithms, Machinery Failure Prevention Technology Conference (MFPT 59), 2005.

J. L. Casti, Nonlinear system theory, Mathematics in Science and Engineering, 1985.

A. Chatterjee, J. P. Cusumano, and D. Chelidze, OPTIMAL TRACKING OF PARAMETER DRIFT IN A CHAOTIC SYSTEM: EXPERIMENT AND THEORY, Journal of Sound and Vibration, vol.250, issue.5, pp.877-901, 2002.
DOI : 10.1006/jsvi.2001.3963

D. Chelidze, A nonlinear observer for damage evolution tracking, 2000.

D. Chelidze, Identifying Multidimensional Damage in a Hierarchical Dynamical System, Nonlinear Dynamics, vol.37, issue.4, pp.307-322, 2004.
DOI : 10.1023/B:NODY.0000045546.02766.ad

D. Chelidze and J. P. Cusumano, A Dynamical Systems Approach to Failure Prognosis, Journal of Vibration and Acoustics, vol.126, issue.1, pp.1-7, 2004.
DOI : 10.1115/1.1640638

D. Chelidze, J. P. Cusumano, and A. Chatterjee, A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application, Journal of Vibration and Acoustics, vol.124, issue.2, pp.250-257, 2002.
DOI : 10.1115/1.1456908

D. Chelidze and M. Liu, Dynamical systems approach to fatigue damage identification, Journal of Sound and Vibration, vol.281, issue.3-5, pp.887-904, 2005.
DOI : 10.1016/j.jsv.2004.02.017
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.667.3811

D. Chelidze and M. Liu, Multidimensional Damage Identification Based on Phase Space Warping: An Experimental Study, Nonlinear Dynamics, vol.230, issue.2, pp.61-72, 2006.
DOI : 10.1007/s11071-005-9007-7

D. Chelidze and M. Liu, Reconstructing slow-time dynamics from fast-time measurements, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.19, issue.11, pp.7429-7445, 2008.
DOI : 10.1103/PhysRevLett.96.118701

D. Chelidze and W. Zhou, Phase space warping: nonlinear time-series analysis for slowly drifting systems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.65, issue.6, pp.2495-2513, 2006.
DOI : 10.1103/PhysRevA.45.3403

D. Chelidze and W. Zhou, Smooth orthogonal decomposition-based vibration mode identification, Journal of Sound and Vibration, vol.292, issue.3-5, pp.461-473, 2006.
DOI : 10.1016/j.jsv.2005.08.006

Z. Chen and D. H. Zhou, Particle filtering based fault prediction of nonlinear systems, IFAC Symposium Proceedings of Safeprocess, 2003.

R. B. Chinnam and P. Baruah, Autonomous diagnostics and prognostics through competitive learning driven HMM-based clustering, Proceedings of the International Joint Conference on Neural Networks, 2003., pp.1-4, 2003.
DOI : 10.1109/IJCNN.2003.1223951

A. Chutinan and B. H. Krogh, Computational techniques for hybrid system verification, IEEE Transactions on Automatic Control, vol.48, issue.1, pp.64-75, 2003.
DOI : 10.1109/TAC.2002.806655

C. Clarotti, A. Lannoy, S. Odin, and H. Procaccia, Detection of equipment aging and determination of the efficiency of a corrective measure, Reliability Engineering & System Safety, vol.84, issue.1, pp.57-64, 2004.
DOI : 10.1016/j.ress.2004.01.005

P. Cocheteux, Contribution à la maintenance proactive par la formalisation du processus de pronostic des performances de systèmes industriels, Thèse de doctorat, 2010.

D. W. Coit and J. R. English, System reliability modeling considering the dependence of component environmental influences, Annual Reliability and Maintainability. Symposium. 1999 Proceedings (Cat. No.99CH36283), pp.214-218, 1999.
DOI : 10.1109/RAMS.1999.744121

J. P. Cusumano, D. Chelidze, and A. Chatterjee, A Dynamical Systems Approach to Damage Evolution Tracking, Part 2: Model-Based Validation and Physical Interpretation, Journal of Vibration and Acoustics, vol.124, issue.2, pp.258-264, 2002.
DOI : 10.1115/1.1456907

M. Darouach, M. Zasadzinski, and L. Boutat-baddas, Discussion on "a comparison of sliding mode and unknown observer for fault reconstruction, European Journal of Control, vol.12, issue.3, pp.261-266, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00105253

M. Darouach, M. Zasadzinski, and S. J. Xu, Full-order observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, vol.39, issue.3, pp.606-609, 1994.
DOI : 10.1109/9.280770
URL : https://hal.archives-ouvertes.fr/hal-00098125

H. R. Depold and F. D. Gass, The Application of Expert Systems and Neural Networks to Gas Turbine Prognostics and Diagnostics, Journal of Engineering for Gas Turbines and Power, vol.121, issue.4, pp.607-613, 1999.
DOI : 10.1115/1.2818515

M. Dievart, Architecture de diagnostic et de pronostic distribuées de Systèmes Techniques Complexes de Grande Dimension, Thèse de doctorat, Institut National Polytechnique de, 2010.

M. Dong and D. He, Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis, European Journal of Operational Research, vol.178, issue.3, pp.858-878, 2007.
DOI : 10.1016/j.ejor.2006.01.041

M. Dong and D. He, A segmental hiden semi-markov model (hsmm)-based diagnostics and prognostics framework and methodology, Mechanical Systems and Signal Processing, pp.2248-2266, 2007.

O. E. Dragomir, R. Gouriveau, F. Dragomir, E. Minca, and N. Zerhouni, Review of prognostic problem in condition-based maintenance, European Control Conference, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00418761

H. Aoufir and D. Bouami, Place des modèles d'optimisation dans le processus d'aide à la décision en maintenance. Revue française de gestion industrielle, pp.61-76, 2003.

M. Koujok, Contribution au pronostic industriel : intégration de la confiance à un modèle prédictif neuro-flou, Thèse de doctorat, 2010.

E. Yaagoubi, A. Assoudi, and H. Hammouri, High gain observer : Attenuation of the peak phenomena, American Control Conference, vol.5, pp.4393-4397, 2004.

R. Engel and G. Kreisselmeier, A continuous-time observer which converges in finite time, IEEE Transactions on Automatic Control, vol.47, issue.7, pp.1202-1204, 2002.
DOI : 10.1109/TAC.2002.800673

S. J. Engel, B. Gilmartin, K. Bongort, and A. Hess, Prognostics, the real issues involved with predicting life remaining, 2000 IEEE Aerospace Conference. Proceedings (Cat. No.00TH8484), pp.457-469, 2000.
DOI : 10.1109/AERO.2000.877920

M. Farza, M. M. Saad, M. Triki, and T. Maatoug, High gain observer for a class of non-triangular systems, Systems & Control Letters, vol.60, issue.1, pp.27-35, 2011.
DOI : 10.1016/j.sysconle.2010.09.009
URL : https://hal.archives-ouvertes.fr/hal-01059914

A. Fatemi and L. Yang, Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials, International Journal of Fatigue, vol.20, issue.1, pp.9-34, 1998.
DOI : 10.1016/S0142-1123(97)00081-9

M. S. Finkelstein, Wearing-out of components in a variable environment, Reliability Engineering & System Safety, vol.66, issue.3, pp.235-242, 1999.
DOI : 10.1016/S0951-8320(99)00023-X

M. Fliess, C. Join, and H. Sira-ramirez, Non-linear estimation is easy, International Journal of Modelling, Identification and Control, vol.4, issue.1, pp.12-27, 2008.
DOI : 10.1504/IJMIC.2008.020996
URL : https://hal.archives-ouvertes.fr/inria-00158855

A. M. Fraser and H. L. Swinney, Independent coordinates for strange attractors from mutual information, Physical Review A, vol.33, issue.2, pp.1134-1140, 1986.
DOI : 10.1103/PhysRevA.33.1134

L. Fridman, Y. Shtessel, C. Edwards, and X. G. Yan, Higher order sliding-mode observer for state estimation and input reconstruction in nonlinear systems, International Journal of Robust and Nonlinear Control, pp.339-412, 2007.

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

A. Girard, Reachability of uncertain linear systems using zonotopes Hybrid Systems : Computation and Control, pp.291-305, 2005.

A. Girard and C. L. Guernic, Efficient Reachability Analysis for Linear Systems using Support Functions, 17th IFAC World Congress, pp.8966-8971, 2008.
DOI : 10.3182/20080706-5-KR-1001.01514
URL : https://hal.archives-ouvertes.fr/hal-00307009

A. Girard, C. L. Guernic, and O. Maler, Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs, Hybrid Systems : Computation and Control, pp.257-271, 2006.
DOI : 10.1007/11730637_21
URL : https://hal.archives-ouvertes.fr/hal-00171555

K. M. Goh, B. Tjahjono, T. Baines, and S. Subramaniam, A Review of Research in Manufacturing Prognostics, 2006 IEEE International Conference on Industrial Informatics, pp.417-422, 2006.
DOI : 10.1109/INDIN.2006.275836

S. Goldman, Vibration spectrum analysis : A practical approach, 1999.

J. L. Gouzé, A. Rapaport, and 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

A. Grall, C. Bérenguer, and L. Dieulle, A condition-based maintenance policy for stochastically deteriorating systems, Reliability Engineering & System Safety, vol.76, issue.2, pp.167-180, 2002.
DOI : 10.1016/S0951-8320(01)00148-X

F. Greitzer and A. Pawlowski, Embedded prognostics health monitoring, 48th Annual Instrumentations, Systems, and Automation Society International Instrumentation Symposium, 2002.

Y. Guan and M. Saif, A novel approach to the design of unknown input observers, IEEE Transactions on Automatic Control, vol.36, issue.5, pp.632-635, 1991.
DOI : 10.1109/9.76372

D. Gucik-derigny, R. Outbib, and M. Ouladsine, Estimation of damage behaviour for model-based-prognosis, 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS'09, 2009.

D. Gucik-derigny, R. Outbib, and M. Ouladsine, Diagnostic prédictif sous contrainte temporelle, Conférence Internationale Francophone d'Automatique, 2010.

D. Gucik-derigny, R. Outbib, and M. Ouladsine, Prognosis applied to an electromechanical system, a nonlinear approach based on high gain observer, IEEE International Conference on Prognostics and Health Management, 2011.

D. Gucik-derigny, R. Outbib, and M. Ouladsine, Prognosis applied to an electromechanical system, a nonlinear approach based on sliding mode observer, Annual Conference on European Safety and Reliability Association, 2011.

D. Gucik-derigny, R. Outbib, and M. Ouladsine, A result on unknown input interval observer design with application to system prognosis, 9 th IEEE International Conference on Control and Automation, 2011.

Q. P. Ha and H. Trinh, State and input simultaneous estimation for a class of nonlinear systems, Automatica, vol.40, issue.10, pp.1779-1785, 2004.
DOI : 10.1016/j.automatica.2004.05.012

J. Llinas, L. D. Hall, and . Fl, Handbook of sensor fusion, 2000.

J. Han and M. Kamber, Data Mining, 2006.
DOI : 10.1007/978-1-4899-7993-3_104-2

A. Heng, S. Zhang, A. Tan, and J. Mathew, Rotating machinery prognostics: State of the art, challenges and opportunities, Mechanical Systems and Signal Processing, pp.724-739, 2009.
DOI : 10.1016/j.ymssp.2008.06.009

F. Hlawatsch and F. Auger, Time frequency analysis : concepts and methods, 2009.
DOI : 10.1002/9780470611203

K. Holmberg, A. Adgar, and A. Arnaiz, E-maintenance, p.511, 2010.
DOI : 10.1007/978-1-84996-205-6
URL : https://hal.archives-ouvertes.fr/hal-00548712

M. Hou and P. C. Müller, Design of observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.871-875, 1992.
DOI : 10.1109/9.256351

D. J. Inman, Damage prognosis : for aerospace, civil and mechanical systems, 2005.
DOI : 10.1002/0470869097

M. R. James, Finite time observers and observability, 29th IEEE Conference on Decision and Control, pp.770-771, 1990.
DOI : 10.1109/CDC.1990.203692

A. Jardine and D. Banjevic, INTERPRETATION OF INSPECTION DATA EMANATING FROM EQUIPMENT CONDITION MONITORING TOOLS: METHOD AND SOFTWARE, Fourth International Conference on Mathematical Methods in Reliability Methodology and Practice, 2004.
DOI : 10.1142/9789812703378_0019

A. Jardine, D. Lin, and D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing, vol.20, issue.7, pp.1483-1510, 2006.
DOI : 10.1016/j.ymssp.2005.09.012

L. Jaulin, I. Braems, M. Kieffer, and E. Walter, Guaranteed non-linear estimation using constraint propagation on sets, International Journal of Control, vol.32, issue.18, pp.1772-1782, 2001.
DOI : 10.1080/00207170110090642

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis, 2001.
DOI : 10.1007/978-1-4471-0249-6
URL : https://hal.archives-ouvertes.fr/hal-00845131

C. D. Johnson, On observers for linear systems with unknown and inaccessible inputs, International Journal of Control, vol.14, pp.825-831, 1975.

T. Johnson and T. Dasu, Data quality and data cleaning, Proceedings of the 2003 ACM SIGMOD international conference on on Management of data , SIGMOD '03, 2003.
DOI : 10.1145/872757.872875

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

G. J. Kacprzynski, M. J. Roemer, A. Modgil, A. Palladino, and K. Maynard, Enhancement of physics-of-failure prognostic models with system level features, Proceedings, IEEE Aerospace Conference, 2002.
DOI : 10.1109/AERO.2002.1036131

G. J. Kacprzynski, A. Sarlashkar, and M. J. Roemer, Predicting remaining useful life by fusing the physics of failure modeling with diagnostics, Journal of Metal, vol.56, pp.29-35, 2004.

R. Kalman, P. L. Falb, and A. Arbib, Topics in mathematical system theory, 1969.

H. Kantz and T. Schreiber, Nonlinear time series analysis, 2004.
DOI : 10.1017/CBO9780511755798

K. Kazmierczak, Application of regressive prognostic techniques in diagnostics, Proceedings of the Vehicle Diagnostics Conference, 1983.

V. A. Kopnov, Optimal degradation processes control by two-level policies. Reliability Engineering and System Safety, pp.1-11, 1999.

R. Kothamasu, S. H. Huang, and W. H. Verduin, System health monitoring and prognostics : a review of current paradigms and practices, The International Journal of Advanced Manufacturing Technology, vol.28, pp.9-101012, 2006.

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

A. B. Kurzhanskiy and P. Varaiya, Ellipsoidal Techniques for Reachability Analysis, Hybrid Systems : Computation and Control, pp.202-214, 2000.
DOI : 10.1007/3-540-46430-1_19

C. Kwan, X. Zhang, R. Xu, and L. Haynes, A novel approach to fault diagnostics and prognostics, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), pp.604-609, 2003.
DOI : 10.1109/ROBOT.2003.1241660

G. Lafferriere, G. J. Pappas, 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

M. Lebold and M. Thurston, Open standards for condition-based maintenance and prognostic systems, Proceedings of the 5th Annual Maintenance and Reliability Conference, 2001.

J. Lee, E-manufacturing???fundamental, tools, and transformation, Robotics and Computer-Integrated Manufacturing, vol.19, issue.6, pp.501-507, 2003.
DOI : 10.1016/S0736-5845(03)00060-7

J. Lee, J. Ni, D. Djurdjanovic, H. Qiu, and H. Liao, Intelligent prognostics tools and e-maintenance, Computers in Industry, vol.57, issue.6, pp.476-489, 2006.
DOI : 10.1016/j.compind.2006.02.014
URL : http://www.sciencedirect.com/science?_ob=ShoppingCartURL&_method=add&_eid=1-s2.0-S0166361506000522&originContentFamily=serial&_origin=article&_ts=1480357466&md5=fb54b9ac8ca52e1d503fb15b5eac4d77

J. Lemaitre, On Course on Damage Mechanics, 1992.
DOI : 10.1007/978-3-642-18255-6

J. Lemaitre and R. Desmorat, Engineering damage mechanics, 2005.

G. A. Lesieutre, L. Fang, and U. Lee, Hierarchical failure simulation for machinery prognostics . Critical Link : Diagnosis to Prognosis, pp.103-110, 1997.

Y. Li, S. Billington, C. Zhang, T. Kurfess, and S. Danyluk, Adaptive prognostics for rolling element bearing condition, Mechanical System and Signal Processing, pp.1483-1510, 1999.
DOI : 10.1006/mssp.1998.0183

Y. Li, T. Kurfess, and S. Y. Liang, STOCHASTIC PROGNOSTICS FOR ROLLING ELEMENT BEARINGS, Mechanical Systems and Signal Processing, vol.14, issue.5, pp.747-762, 2000.
DOI : 10.1006/mssp.2000.1301

F. L. Liu, M. Farza, and M. M. Saad, Nonlinear observers for state and unknown inputs estimation, International Journal of Modelling, Identification and Control, pp.24-32, 2007.

M. Liu and D. Chelidze, Identifying damage using local flow variation method, Smart Materials and Structures, vol.15, issue.6, pp.1830-1836, 2006.
DOI : 10.1088/0964-1726/15/6/037

J. Luo, K. R. Pattipati, L. Qiao, and S. Chigusa, Model-based prognostic techniques applied to a suspension system, PART A : Systems and Humans, pp.1156-1168, 2008.

S. Mallat, A wavelet tour of signal processing : the sparse way, 2009.

F. Mazenc and O. Bernard, Asymptotically Stable Interval Observers for Planar Systems With Complex Poles, IEEE Transactions on Automatic Control, vol.55, issue.2, pp.523-527, 2010.
DOI : 10.1109/TAC.2009.2037472
URL : https://hal.archives-ouvertes.fr/hal-00547800

F. Mazenc and O. Bernard, Interval observers for linear time-invariant systems with disturbances, Automatica, vol.47, issue.1, pp.140-147, 2010.
DOI : 10.1016/j.automatica.2010.10.019
URL : https://hal.archives-ouvertes.fr/hal-00555464

M. Mboup, C. Join, and M. Fliess, Numerical differentiation with annihilators in noisy environment, Numerical Algorithms, vol.14, issue.12, pp.439-467, 2009.
DOI : 10.1007/s11075-008-9236-1
URL : https://hal.archives-ouvertes.fr/inria-00319240

J. S. Meditch and G. H. Hostetter, Observers for systems with unknown and inaccessible inputs???, International Journal of Control, vol.15, issue.3, pp.473-480, 1974.
DOI : 10.1080/00207177408932644

T. Menard, E. Moulay, and W. Perruquetti, A Global High-Gain Finite-Time Observer, IEEE Transactions on Automatic Control, vol.55, issue.6, pp.1500-1506, 2010.
DOI : 10.1109/TAC.2010.2045698
URL : https://hal.archives-ouvertes.fr/hal-00455790

P. H. Menold, Finite time and asymptotic time state estimation for linear and nonlinear systems, 2004.

P. H. Menold, R. Findeisen, and F. Allgöwer, Finite time convergent observers for linear time-varying systems, Proceedings of the Mediterranean Conference on Control and Automation, 2003.

P. H. Menold, R. Findeisen, and F. Allgöwer, Finite time convergent observers for nonlinear systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003.
DOI : 10.1109/CDC.2003.1271908

M. A. Miner, Cumulative damage in fatigue, Journal of Applied Mechanics, vol.12, issue.3, pp.159-164, 1945.

M. Müller, ???ber das Fundamentaltheorem in der Theorie der gew???hnlichen Differentialgleichungen, Mathematische Zeitschrift, vol.10, issue.4, pp.619-645, 1926.
DOI : 10.1007/BF01475477

S. Moaveni, Finite element analysis : theory and application with ANSYS, 2008.

M. Moisan and O. Bernard, INTERVAL OBSERVERS FOR NON MONOTONE SYSTEMS. APPLICATION TO BIOPROCESS MODELS, 16th IFAC world Conference, 2005.
DOI : 10.3182/20050703-6-CZ-1902.02211

M. Moisan and O. Bernard, Semi-global finite-time observers for nonlinear systems, Automatica, vol.44, issue.12, pp.3152-3156, 2008.

M. Moisan and O. Bernard, Robust interval observers for global Lipschitz uncertain chaotic systems, Systems & Control Letters, vol.59, issue.11, pp.687-694, 2010.
DOI : 10.1016/j.sysconle.2010.08.005

M. Moisan, O. Bernard, and J. L. Gouzé, Near optimal interval observers bundle for uncertain bioreactors, Automatica, vol.45, issue.1, pp.291-295, 2009.
DOI : 10.1016/j.automatica.2008.07.006
URL : https://hal.archives-ouvertes.fr/hal-01109396

E. Moulay and W. Perruquetti, Finite time stability and stabilization of a class of continuous systems, Journal of Mathematical Analysis and Applications, vol.323, issue.2, pp.1430-1443, 2003.
DOI : 10.1016/j.jmaa.2005.11.046

E. Moulay and W. Perruquetti, Finite time stability of nonlinear systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.3641-3646, 2003.
DOI : 10.1109/CDC.2003.1271714

A. Muller, Contribution à la maintenance prévisionnelle des systèmes de production par la formalisation d'un processus de pronostic, Thèse de doctorat, 2005.

C. H. Oppenheimer and K. A. Loparo, Physically based diagnosis and prognosis of cracked rotor shafts. Component and Systems Diagnostics, Prognostics and Health Management II, pp.122-132, 2002.

M. Orchard, B. Wu, and G. Vachtsevanos, A Particle Filtering Framework for Failure Prognosis, World Tribology Congress III, Volume 2, 2005.
DOI : 10.1115/WTC2005-64005

M. E. Orchard, A particle Filtering-based Framework for On-line Fault Diagnosis and Failure Prognosis, 2006.

R. Ouladsine and R. Outbib, A probabilistic approach for prognosis of complex systems, 1 st IEEE Australian Control Conference 2011, 2011.

R. Ouladsine and R. Outbib, Prognosis of complex systems by analysis damage trajectory, 9 th IEEE International Conference on Control and Automation, 2011.

R. Outbib and D. Gucik-derigny, Prognosis of systems : concept, methodologies and application, 2011.

K. Passino and K. Burgess, Stability analysis of discrete event systems, 1998.

R. Patrick-adalco, A Model Based Framework for Fault Diagnosis and Prognosis of Dynamical Systems with an application to Helicopter Transmissions, 2007.

F. Peysson, Contribution au pronostic des systèmes complexes, Thèse de doctorat, 2009.

F. Peysson, M. Ouladsine, R. Outbib, J. B. Leger, O. Myx et al., A Generic Prognostic Methodology Using Damage Trajectory Models, IEEE Transactions on Reliability, vol.58, issue.2, pp.277-285, 2009.
DOI : 10.1109/TR.2009.2020123

A. G. Piersol, T. L. Paez, and C. M. Harris, Harris'shock and vibration handbook, 2009.

J. Qiu, C. Zhang, B. B. Seth, and S. Y. Liang, DAMAGE MECHANICS APPROACH FOR BEARING LIFETIME PROGNOSTICS, Mechanical Systems and Signal Processing, vol.16, issue.5, pp.817-829, 2002.
DOI : 10.1006/mssp.2002.1483

T. Raff, F. Lachner, and F. Allgower, A Finite Time Unknown Input Observer For Linear Systems, 2006 14th Mediterranean Conference on Control and Automation, 2006.
DOI : 10.1109/MED.2006.328795

S. Rao, Reliability based design, 1992.

A. Rapaport and J. L. Gouze, Parallelotopic and practical observers for non-linear uncertain systems, International Journal of Control, vol.76, issue.3, pp.237-251, 2003.
DOI : 10.1109/TAC.1968.1098790
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.5788

I. Rasovska, B. Chebel-morello, and N. Zerhouni, Classification des différentes architectures en maintenance. 7e Congrès international de génie industriel, Trois-Rivières, pp.1-12, 2007.

T. Raïssi, D. Efimov, and A. Zolghadri, Asymptotically stable interval observers for planars systems with complex poles, Automatica, 2011.

A. Ray and S. Tangirala, Stochastic modeling of fatigue crack dynamics for on-line failure prognostics, IEEE Transactions on Control Systems Technology, vol.4, issue.4, pp.443-451, 1996.
DOI : 10.1109/87.508893

E. Reynaud, Développement durable et entreprise : vers une solution symbiotique, Journée AIMS, Atelier Développement durable, pp.1-15, 2003.

P. Ribot, Vers l'intégration diagnostic/pronostic pour la maintenance des systèmes complexes, Thèse de doctorat, 2009.

M. J. Roemer, C. Byington, G. J. Kacprzinski, and G. Vachtsevanos, An overview of selected technologies with reference to integrated phm architecture, First International Forum on Integrated System Health Engineering and Management in Aerospace, 2005.

M. J. Roemer, E. Nwadiogbu, and G. Bloor, Development of diagnostic and prognostic technologies for aerospace health management applications, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542), pp.3139-3147, 2001.
DOI : 10.1109/AERO.2001.931331

A. Saxena, J. Celaya, E. Balaban, S. Saha, B. Saha et al., Metrics for evaluating performance of prognostic techniques, 2008 International Conference on Prognostics and Health Management, 2008.
DOI : 10.1109/PHM.2008.4711436

A. Saxena, J. Celaya, B. Saha, S. Saha, and K. Goebel, On applying the prognostic perfomance metrics, Proceedings of the 1th Annual Conference of the Prognostics and Health Management Society, 2009.

H. L. Smith, Monotone dynamical systems : an introduction to the theory of competitive and cooperative systems, 1995.
DOI : 10.1090/surv/041

O. Sénéchal, Pilotage des systèmes de production vers la performance globale, Habilitation à diriger des Recherches, Thèse de doctorat, 2004.

E. Sontag, Mathematical control theory : deterministic finite dimensional systems, 1998.

A. N. Steinberg and C. L. Bowman, Revisions to the jdl data fusion model, Proceedings of the third NATO/IRIS conference, 1998.

D. C. Swanson, A general prognostic tracking algorithm for predictive maintenance, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542), pp.2971-2977, 2001.
DOI : 10.1109/AERO.2001.931317

L. Swanson, Linking maintenance strategies to performance, International Journal of Production Economics, vol.70, issue.3, pp.237-244, 2001.
DOI : 10.1016/S0925-5273(00)00067-0

K. Swearingen, W. Majkowski, B. Bruggeman, D. Gilbertson, J. Dunsdon et al., An Open System Architecture for Condition Based Maintenance Overview, 2007 IEEE Aerospace Conference, pp.1-8, 2007.
DOI : 10.1109/AERO.2007.352921

M. Triki, Synthèse d'observateurs pour des classes de systèmes non linéaires, Thèse de doctorat, 2011.

G. Vachtsevanos, Performance metrics for fault prognosis of complex systems, Proceedings AUTOTESTCON 2003. IEEE Systems Readiness Technology Conference., pp.341-345, 2003.
DOI : 10.1109/AUTEST.2003.1243597

G. Vachtsevanos, F. Lewis, M. Roemer, A. Hess, and B. Wu, Intelligent Fault Diagnosis and Prognosis for Engineering Systems, 2006.
DOI : 10.1002/9780470117842

O. Vasile, Contribution au pronostic de défaillances par réseau neuro-flou : maîtrise de l'erreur de prédiction, Thèse de doctorat, 2008.

V. Venkatasubramanian, R. Raghunathan, and S. N. Kavuri, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.313-326, 2003.
DOI : 10.1016/S0098-1354(02)00161-8

V. Venkatasubramanian, R. Raghunathan, S. N. Kavuri, and K. Yin, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.327-346, 2003.
DOI : 10.1016/S0098-1354(02)00162-X

V. Venkatasubramanian, R. Raghunathan, and K. Yin, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.293-311, 2003.
DOI : 10.1016/S0098-1354(02)00160-6

N. M. Vichare and M. G. Pecht, Prognostics and health management of electronics, IEEE Transactions on Components and Packaging Technologies, vol.29, issue.1, pp.222-229, 2006.
DOI : 10.1109/TCAPT.2006.870387

W. Wang, F. Golnaraghi, and F. Ismail, A robust prognostic system for real-time industrial applications, 4th International Conference on Industrial Automation, 2003.

X. Wang, Y. Gang, M. Koc, and J. Lee, Wavelet neural network for machining performance assessment and its implications to machinery prognostics, 54th International Conference on Managing Innovations in Manufacturing, 2002.

T. Wireman, Developing performance indicators for managing maintenance. Industrial press, 2005.

Y. Xiong and M. Saïf, Unknown disturbance inputs estimation based on a state functional observer design, Automatica, vol.39, issue.8, pp.1389-1398, 2003.
DOI : 10.1016/S0005-1098(03)00087-6

T. Yan, T. Lee, and M. Koç, Predictive algorithm for machine degradation detection using logistic regression. In Managing innovative manufacturing "e-Manufacturing and e-Business integration, 2002.

F. Yang and R. W. Wilde, Observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control, vol.33, issue.7, pp.677-681, 1988.
DOI : 10.1109/9.1278

S. K. Yang, An experiment of state estimation for predictive maintenance using Kalman filter on a DC motor, Reliability Engineering & System Safety, vol.75, issue.1, pp.338-353, 2002.
DOI : 10.1016/S0951-8320(01)00107-7

A. Zemouri, Contribution à la surveillance des systèmes de production à l'aide de réseaux de neurones dynamiques : Application à la e-maintenance, Thèse de doctorat, 2003.

M. Zemouri, D. Racoceanu, and N. Zerhouni, Réseaux de neurones récurrents à fonctions à bases radiales : Rrfr, application au pronostic. Revue d'intelligence artificielle, RSTI série RIA, pp.307-338, 2002.
DOI : 10.3166/ria.16.307-338

X. Zhang, R. Xu, C. Kwan, S. Y. Liang, Q. Xie et al., An integrated approach to bearing fault diagnostics and prognostics, Proceedings of American Control Conference, pp.2750-2755, 2005.

V. Zille, Modélisation et évaluation des stratégies de maintenance complexes sur des systèmes multi-composants, Thèse de doctorat, 2009.