G. A. Ackerson and K. S. Fu, On state estimation in switching environments, IEEE Transactions on Automatic Control, vol.15, issue.1, pp.10-17, 1970.
DOI : 10.1109/TAC.1970.1099359

O. Adrot, Diagnostic à base de modèles incertains utilisant l'analyse par intervalle : l'approche bornante, 2000.

A. Alessandri and P. Coletta, Design of Luenberger Observers for a Class of Hybrid Linear Systems, Proceedings of Hybrid Systems : Computation and Control, 2001.
DOI : 10.1007/3-540-45351-2_5

A. Alessandri and P. Coletta, Switching observers for continuous-time and discrete-time linear systems, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.2516-2521, 2001.
DOI : 10.1109/ACC.2001.946132

A. Alessandri and P. Coletta, Design of observers for switched discrete-time linear systems, Proceedings of the 2003 American Control Conference, 2003., pp.2785-2790, 2003.
DOI : 10.1109/ACC.2003.1243744

M. Babaali and M. Egerstedt, Hybrid Systems : Computation and Control, 2004.

. Chap, Observability of switched linear systems, Lecture Notes in Computer Science, pp.48-63

M. Babaali, M. Et, and . Egerstedt, ASYMPTOTIC OBSERVERS FOR DISCRETE-TIME SWITCHED LINEAR SYSTEMS, Proceedings of 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00212

A. Balluchi, L. Benvenuti, M. D. Di-benedetto, and A. L. Sangiovanni-vincentelli, A hybrid observer for the driveline dynamics, Proceedings of the European Control Conference, pp.618-623, 2001.

A. Balluchi, L. Benvenuti, M. D. Di-benedetto, and A. L. Sangiovanni-vincentelli, Design of Observers for Hybrid Systems, Proceedings of Hybrid Systems : Computation and Control, pp.76-89, 2002.
DOI : 10.1007/3-540-45873-5_9

I. G. Bara, J. Daafouz, F. Kratz, and C. Iung, State estimation for a class of hybrid systems, Proceedings of 4th International Conference on Automation of Mixed Processes : Hybrid Dynamic Systems, pp.313-316, 2000.

M. Basseville, I. V. Et, and . Nikiforov, Detection of abrupt changes -Theory and application. Information and System Sciences Series, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00008518

R. Batruni, A multilayer neural network with piecewise-linear structure and back-propagation learning, IEEE Transactions on Neural Networks, vol.2, issue.3, pp.395-403, 1991.
DOI : 10.1109/72.97915

R. V. Beard, Failure accomodation in linear system trhough selfreorganisation, Dept. of Aero. and Astro, 1971.

A. Bemporad, A. Garulli, S. Paoletti, and A. Vicino, Hybrid Systems : Computation and Control. Chap. A greedy approach to identification to identification of piecewise affine models, Lecture Notes in Computer Science, 2003.

A. Bemporad, D. Mignone, and M. Morari, Fault detection and state estimation for hybrid system, Proceedings of the American Control Conference, pp.2471-2475, 1999.

A. Bemporad and M. Morari, Control of systems integrating logic, dynamics, and constraints, Automatica, vol.35, issue.3, pp.407-427, 1999.
DOI : 10.1016/S0005-1098(98)00178-2

A. Bemporad, G. Ferrari-trecate, and M. Morari, Observability and controllability of piecewise affine and hybrid systems, IEEE Transactions on Automatic Control, vol.45, issue.10, pp.1864-1876, 2000.
DOI : 10.1109/TAC.2000.880987

Y. Ben-haim, An Algorithm for Failure Location in a Complex Network, Nuclear Science and Engineering, vol.75, issue.2, pp.191-199, 1980.
DOI : 10.13182/NSE80-A21310

K. P. Bennett, E. J. Et, and . Bredensteiner, Geometry at work. Chap. Geometry in learning, 1993.

K. P. Bennett, O. L. Et, and . Mangasarian, Multicategory discrimination via linear programming. Optimization Methods and Software 3, pp.27-39, 1994.
DOI : 10.1080/10556789408805554

URL : https://minds.wisconsin.edu/bitstream/handle/1793/59684/TR1127.pdf?sequence=1

S. A. Billings and W. S. Voon, Piecewise linear identification of non-linear systems, International Journal of Control, vol.59, issue.1, pp.215-235, 1987.
DOI : 10.1111/j.1467-9892.1980.tb00300.x

P. Biswas, P. Grieder, J. Löfberg, and M. Morari, A SURVEY ON STABILITY ANALYSIS OF DISCRETE-TIME PIECEWISE AFFINE SYSTEMS, Proceedings of the 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.00332

V. Blondel, J. N. Et, and . Tsitsiklis, 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

J. F. Bonnans, J. Ch, C. Gilbert, C. A. Lemarchal, and . Sagastizbal, Numerical optimization : theoretical and practical aspects, 2002.
DOI : 10.1007/978-3-662-05078-1

E. J. Bredensteiner, K. P. Et, and . Bennett, Multicategory Classification by Support Vector Machines, Computational Optimization and Applications, vol.12, pp.53-79, 1999.
DOI : 10.1007/978-1-4615-5197-3_5

URL : http://www.rensselaer.edu/~bennek/main3.ps

L. Breiman, Hinging hyperplanes for regression, classification, and function approximation, IEEE Transactions on Information Theory, vol.39, issue.3, pp.999-1013, 1993.
DOI : 10.1109/18.256506

K. S. Chan and H. Tong, ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS, Journal of Time Series Analysis, vol.37, issue.3, pp.179-190, 1986.
DOI : 10.1007/978-1-4684-7888-4

J. Chen, R. J. Patton, and H. Y. Zhang, Design of robust structured and directional residuals for fault isolation via unknow input observers, Proceedings of the 3rd European Control Conference, pp.348-353, 1995.

C. Choi, J. Y. Et, and . Choi, Constructive neural networks with piecewise interpolation capabilities for function approximations, IEEE Transactions on Neural Networks, vol.5, issue.6, pp.936-944, 1994.
DOI : 10.1109/72.329691

B. Chow and E. Y. , A failure detection system design methodology, 1980.

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

L. O. Chua, S. M. Et, and . Kang, Section-wise piecewise-linear functions: Canonical representation, properties, and applications, Proceedings of the IEEE, 1977.
DOI : 10.1109/PROC.1977.10589

V. Cocquempot, M. Staroswiecki, and T. Mezyani, Switching Time Estimation and Fault Detection for Hybrid Systems Using Structured Parity Residuals, IFAC Proceedings Volumes, vol.36, issue.5, 2003.
DOI : 10.1016/S1474-6670(17)36563-1

D. Schutter and B. , Optimal Control of a Class of Linear Hybrid Systems with Saturation, SIAM Journal on Control and Optimization, vol.39, issue.3, pp.835-851, 2000.
DOI : 10.1137/S0363012999354648

D. Schutter, B. Et, T. J. Van-den, and . Boom, Model predictive control for maxmin-plus-scaling systems, Proceedings of the American Control Conference, 2001.

A. Doucet, A. Logothetis, and V. Krishnamurthy, Particle filters for state estimation of jump Markov linear systems, IEEE Transactions on Signal Processing, vol.49, issue.3, pp.613-624, 2001.
DOI : 10.1109/78.905890

S. Ernst, Hinging hyperplane trees for approximation and identification, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998.
DOI : 10.1109/CDC.1998.758452

J. S. Evans, R. J. Et, and . Evans, Image-enhanced multiple model tracking, Automatica, vol.35, issue.11, pp.1769-1786, 1999.
DOI : 10.1016/S0005-1098(99)00086-2

URL : http://degas.eecs.berkeley.edu/~jse/pubs/iemmt.ps.gz

R. C. Fair, D. M. Et, and . Jafeee, Methods of Estimation for Markets in Disequilibrium, Econometrica, vol.40, issue.3, pp.299-308, 1972.
DOI : 10.2307/1913181

G. Ferrari-trecate, D. Mignone, and M. Morari, Moving horizon estimation for hybrid systems, IEEE Transactions on Automatic Control, vol.47, issue.10, pp.1663-1676, 2002.
DOI : 10.1109/TAC.2002.802772

G. Ferrari-trecate, M. Muselli, D. Liberati, and M. Morari, A clustering technique for the identification of piecewise affine systems, Automatica, vol.39, issue.2, pp.205-217, 2003.
DOI : 10.1016/S0005-1098(02)00224-8

D. Filev, Fuzzy modeling of complex systems, International Journal of Approximate Reasoning, vol.5, issue.3, pp.281-290, 1991.
DOI : 10.1016/0888-613X(91)90013-C

E. F. Gad, A. F. Atiya, S. Shaheen, and A. El-dessouki, A new algorithm for learning in piecewise-linear neural networks, Neural Networks, vol.13, issue.4-5, pp.4-5, 2000.
DOI : 10.1016/S0893-6080(00)00024-1

K. Gasso, G. Mourot, and J. Ragot, STRUCTURE IDENTIFICATION OF MULTIPLE MODELS WITH OUTPUT ERROR LOCAL MODELS, Proceedings of 15th IFAC World Congress on Automatic Control, 2002.
DOI : 10.3182/20020721-6-ES-1901.01011

URL : https://hal.archives-ouvertes.fr/hal-00975105

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

J. J. Gertler, Structured residuals for fault isolation, disturbance decoupling and modeling error robustness, Proceedings of the IFAC symposium on-line Fault Detection and Supervision in the Chemical Processes Industries, pp.111-119, 1992.

J. J. Gertler, Optimal residual decoupling for robust fault diagnosis, International Journal of Control, vol.3, issue.2, pp.395-421, 1995.
DOI : 10.1109/TAC.1987.1104682

J. J. Gertler, R. Et, and . Monajemy, Generating Directional Residuals with Dynamic Parity Equations *, Proceedings of the 12th IFAC World Congress, 1993.
DOI : 10.1016/S1474-6670(17)48318-2

S. M. Goldfeld, R. E. Et, and . Quandt, A Markov model for switching regressions, Journal of Econometrics, vol.1, issue.1, pp.3-16, 1973.
DOI : 10.1016/0304-4076(73)90002-X

D. Goshen-meskin and I. Y. Et, Observability analysis of piece-wise constant systems. I. Theory, IEEE Transactions on Aerospace and Electronic Systems, vol.28, issue.4, pp.1056-1067
DOI : 10.1109/7.165367

C. W. Granger, R. Et, and . Ramanathan, Improved methods of combining forecasts, Journal of Forecasting, vol.62, issue.2, pp.197-204, 1984.
DOI : 10.1002/for.3980030207

C. W. Granger, T. Et, and . Terasvirta, Modelling nonlinear economic relationships, 1993.

P. Grieder, M. Et, and . Morari, Complexity reduction of receding horizon control, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003.
DOI : 10.1109/CDC.2003.1273112

P. Grieder, M. Kvasnica, M. Baoticét, and M. Morari, Low complexity control of piecewise affine systems with stability guarantee, Proceedings of the American Control Conference, 2004.

P. Grieder, P. Parillo, and M. Morari, Robust horizon receding control -analyis and synthesis, Proceedings of the 42th IEEE Conference on Decison and Control, 2003.
DOI : 10.1109/cdc.2003.1272688

F. Hamelin, D. Sauter, and M. Aubrun, Fault diagnosis in systems using directional residuals, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.3040-3045, 1994.
DOI : 10.1109/CDC.1994.411320

J. D. Hamilton, A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle, Econometrica, vol.57, issue.2, pp.357-384, 1989.
DOI : 10.2307/1912559

J. D. Hamilton, Analysis of time series subject to changes in regime, Journal of Econometrics, vol.45, issue.1-2, pp.39-70, 1990.
DOI : 10.1016/0304-4076(90)90093-9

W. P. Heemels, J. M. Schumacher, and S. Weiland, Linear Complementarity Systems, SIAM Journal on Applied Mathematics, vol.60, issue.4, pp.1234-1269, 2000.
DOI : 10.1137/S0036139997325199

URL : https://hal.archives-ouvertes.fr/hal-00834580

E. A. Heredia and G. R. Arce, Piecewise linear system modeling based on a continuous threshold decomposition, IEEE Transactions on Signal Processing, vol.44, issue.6, pp.1440-1453, 1996.
DOI : 10.1109/78.506610

D. J. Hudson, Fitting Segmented Curves Whose Join Points Have to Be Estimated, Journal of the American Statistical Association, vol.15, issue.316, pp.1097-1129, 1966.
DOI : 10.1080/01621459.1964.10480712

D. R. Hush, B. Et, and . Horne, Efficient algorithms for function approximation with piecewise linear sigmoidal networks, IEEE Transactions on Neural Networks, vol.9, issue.6, pp.1129-1141, 1998.
DOI : 10.1109/72.728357

I. Hwang, H. Balakrishnan, and C. Tomlin, Observability criteria and estimator design for stochastic linear hybrid systems, Proceedings of the IEE European Control Conference, 2003.

R. Isermann, Estimation of physical parameters for dynamic processes with application to an industrial robot, International Journal of Control, vol.46, issue.6, pp.1287-1298, 1992.
DOI : 10.1007/978-3-642-82336-7

A. H. Jazwinski, Stochastic processes and filtering theory, 1970.

Y. Ji and H. Chizeck, Controllability, observability and discrete-time markovian jump linear quadratic control, International Journal of Control, vol.48, issue.2, pp.481-498, 1988.
DOI : 10.1016/S0167-6911(81)80008-4

T. A. Johansen, A. B. Et, and . Foss, Constructing NARMAX models using ARMAX models, International Journal of Control, vol.42, issue.5, pp.1125-1153, 1993.
DOI : 10.1080/00207179208934316

P. Julián, A. Desages, and O. Amgamennoni, High-level canonical piecewise linear representation using a simplicial partition, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.46, issue.4, pp.463-480, 1999.
DOI : 10.1109/81.754847

P. Julián, M. Jordan, and A. Desages, Canonical piecewise-linear approximation of smooth functions, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.45, issue.5, pp.567-571, 1998.
DOI : 10.1109/81.668868

A. Juloski, M. Heemels, and G. Ferrari-trecate, Data-based hybrid modelling of the component placement process in pick-and-place machines, Control Engineering Practice, vol.12, issue.10, pp.1241-1252, 2004.
DOI : 10.1016/j.conengprac.2004.04.004

A. Juloski, M. Heemels, G. Ferrari-trecate, R. Vidal, S. Paoletti et al., Hybrid Systems : Computation and Control. Chap. Comparison of Four Bibliographie Procedures for Identification of Hybrid Systems, Lecture Notes on Computer Science, vol.3141, 2005.

A. Juloski, M. Heemels, Y. Boers, and F. Veschure, Two approaches to state estimation for a class of piecewise affine systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.143-148, 2003.
DOI : 10.1109/CDC.2003.1272550

M. A. Kang and L. O. Chua, A global representation of multidimensional piecewise-linear functions with linear partitions, IEEE Transactions on Circuits and Systems, vol.25, issue.11, pp.938-940, 1978.
DOI : 10.1109/TCS.1978.1084401

F. Kratz, D. Et, and . Aubry, Finite Memory Observer for State Estimation of Hybrid System, Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, pp.687-691, 2003.
DOI : 10.1016/S1474-6670(17)36564-3

V. Krishnamurthy, R. J. Et, and . Elliott, Filters for estimating Markov modulated poisson processes and image-based tracking, Automatica, vol.33, issue.5, pp.821-833, 1997.
DOI : 10.1016/S0005-1098(96)00257-9

V. Krishnamurthy, F. Vazquez-abad, and K. Martin, Adaptive nonlinear filters for narrow-band interference suppression in spread-spectrum CDMA systems, IEEE Transactions on Communications, vol.47, issue.5, pp.742-753, 1999.
DOI : 10.1109/26.768768

J. C. Lagarias, Y. Et, and . Wang, The finiteness conjecture for the generalized spectral radius of a set of matrices, Linear Algebra and its Applications, vol.214, pp.17-42, 1995.
DOI : 10.1016/0024-3795(93)00052-2

D. Liberzon, A. S. Et, and . Morse, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine, vol.19, issue.5, pp.59-70, 1999.
DOI : 10.1109/37.793443

D. Liberzon, J. P. Hespanha, and A. S. Morse, Stability of switched systems: a Lie-algebraic condition, Systems & Control Letters, vol.37, issue.3, pp.117-122, 1999.
DOI : 10.1016/S0167-6911(99)00012-2

O. L. Mangasarian, Arbitrary-norm separating plane, Operations Research Letters, vol.24, issue.1-2, pp.15-23, 1999.
DOI : 10.1016/S0167-6377(98)00049-2

URL : https://minds.wisconsin.edu/bitstream/handle/1793/66043/97-07.pdf?sequence=1

D. Maquin, Cours de Master Automatique, Diagnostic, Signal, Bio- Imagerie : Surveillance des Processus, 2005.

M. Mariton, Stochastic observability of linear systems with Markovian jumps, 1986 25th IEEE Conference on Decision and Control, 1986.
DOI : 10.1109/CDC.1986.267479

M. C. Medeiros, A. Veiga, and M. G. Resende, A Combinatorial Approach to Piecewise Linear Time Series Analysis, Journal of Computational and Graphical Statistics, vol.11, issue.1, pp.236-258, 2002.
DOI : 10.1198/106186002317375712

E. Münz, V. Et, and . Krebs, IDENTIFICATION OF HYBRID SYSTEMS USING A PRIORI KNOWLEDGE, Proceedings of the 15th IFAC World Congress, 2002.
DOI : 10.3182/20020721-6-ES-1901.00563

T. Murray-smith and . Johansen, Multiple model approaches to modelling and control, 1997.

S. Paoletti, Identification of Piecewise Affine Models, 2004.

R. J. Patton, Robust model-based fault detection : the state of art, Proceedings of IFAC Symposium on Fault Detection, Supervision and Safety for- Technical Processes, SAFEPROCESS'94, pp.359-367, 1994.

R. J. Patton, P. M. Frank, and R. N. Clark, Issues of Fault Diagnosis for Dynamic Systems, 2000.
DOI : 10.1007/978-1-4471-3644-6

R. J. Patton, P. M. Frank, and R. N. Clark, Fault diagnosis in dynamic systems : theory and application, International Series in Systems and Control Engineering, 1989.

J. E. Potter, M. C. Et, and . Suman, Thresholdless redundancy management with array of skewed instruments, Integrity in Electronic Flight Control Systems, p.224, 1977.

B. Potter and S. M. , A nonlinear approach to US GNP, Journal of Applied Econometrics, vol.1, issue.2, pp.109-125, 1995.
DOI : 10.1007/978-1-4684-7888-4

P. Pucar, J. Et, and . Sjöberg, On the hinge-finding algorithm for hingeing hyperplanes, IEEE Transactions on Information Theory, vol.44, issue.3, pp.1310-1319, 1998.
DOI : 10.1109/18.669422

R. E. Quandt, The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes, Journal of the American Statistical Association, vol.42, issue.284, pp.873-880, 1958.
DOI : 10.1080/01621459.1958.10501484

J. Ragot, Cours de Master Automatique, Diagnostic, Signal, Bio-Imagerie : Estimation d'état. Application au diagnostic, 2005.

J. Ragot, D. Maquin, and E. A. Domlan, Switching Time Estimation of Piecewise Linear Systems. Application to Diagnosis, Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, 2003.
DOI : 10.1016/S1474-6670(17)36566-7

URL : https://hal.archives-ouvertes.fr/hal-00278200

J. Ragot, G. Mourot, and D. Maquin, Parameter estimation of switching piecewise linear system, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.5783-5788, 2003.
DOI : 10.1109/CDC.2003.1271927

URL : https://hal.archives-ouvertes.fr/hal-00151306

J. Roll, Local and Piecewise affine Approaches to System Identification, 2003.

F. Rosenqvist, A. Et, and . Karlström, Realisation and estimation of piecewise-linear output-error models, Automatica, vol.41, issue.3, pp.545-551, 2005.
DOI : 10.1016/j.automatica.2004.11.011

S. Simani, C. Fantuzzi, and R. J. Patton, Model-based Fault Diagnosis in Dynamic Systems Using Identification Techniques, 2003.
DOI : 10.1007/978-1-4471-3829-7

A. Skeppstedt, L. Ljung, A. Benveniste, B. Deylon, P. Glorennec et al., Construction of composite models from observed data, International Journal of Control, vol.38, issue.1, pp.141-152, 1992.
DOI : 10.1080/00207178708933866

E. D. Sontag, Nonlinear regulation: The piecewise linear approach, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.346-358, 1981.
DOI : 10.1109/TAC.1981.1102596

E. D. Sontag, Hybrid Systems III ? Verification and Control. Chap. Interconnected automata and linear systems : a theoretical framework in discretetime, of Lecture Notes in Computer Science, pp.436-448, 1996.

J. Strömberg, F. Gustafsson, and L. Ljung, Trees as black-box model structures for dynamical systems, Proceedings of the European Control Conference, 1991.

H. Tong, Threshold models in non-linear time series analysis, 1983.
DOI : 10.1007/978-1-4684-7888-4

J. K. Tugnait, Detection and estimation for abruptly changing systems, Automatica, vol.18, issue.5, pp.607-615, 1982.
DOI : 10.1016/0005-1098(82)90012-7

A. J. Van-der-schaft, J. M. Et, and . Schumacher, Complementarity modeling of hybrid systems, IEEE Transactions on Automatic Control, vol.43, issue.4, pp.483-490, 1998.
DOI : 10.1109/9.664151

V. N. Vapnik, The nature of statistical learning theory, 1995.

R. Vidal, A. Chiuso, and S. Soatto, Observability and identifiabilty of jump linear systems, Proceedings of the 41st IEEE Conference on Decision and Control, pp.3614-3619, 2002.

R. Vidal, S. Soatto, Y. Ma, and S. Sastry, An algebraic geometric approach to the identification of a class of linear hybrid systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.167-172, 2003.
DOI : 10.1109/CDC.2003.1272554

P. D. West, A. H. Et, and . Haddad, On the observability of linear stochastic switching systems, Proceedings of 1994 American Control Conference, ACC '94, 1994.
DOI : 10.1109/ACC.1994.752392