M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault- Tolerant Control, 2006.

A. F. Colombo, P. Lee, and B. W. Karney, A selective literature review of transient-based leak detection methods, Journal of Hydro-environment Research, vol.2, issue.4, pp.212-227, 2009.
DOI : 10.1016/j.jher.2009.02.003

M. V. Dyke, An Album of Fluid Motion, 1982.

L. Torres, G. Besançon, and D. Georges, A collocation model for water-hammer dynamics with application to leak detection, 2008 47th IEEE Conference on Decision and Control, 2008.
DOI : 10.1109/CDC.2008.4739304

URL : https://hal.archives-ouvertes.fr/hal-00348367

L. Torres, G. Besançon, and D. Georges, A nonlinear observer approach for parameter estimation in chaotic systems, 2010.

M. H. Chaudry, Applied Hydraulic Transients, 1979.
DOI : 10.1007/978-1-4614-8538-4

A. Y. Allidina and A. Benkherouf, Leak detection and location in gas pipelines, Control Theory and Applications IEE Proceedings D, vol.135, issue.2, pp.142-148, 1988.

J. V. Villadsen and W. E. Stewart, Solution of boundary value problems by orthogonal collocation, International Journal of Mathematics and computers in simulation, vol.1, issue.4, pp.350-355, 2007.

J. F. Dulhoste, D. Georges, and G. Besançon, Nonlinear control of openchannel water flow based on collocation control model, Journal of Hydraulic Engineering, vol.30, issue.3, pp.254-266, 2004.

K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, An Introduction, 2005.

C. A. Fletcher, Computational Garlekin Methods, 1984.

J. F. Dulhoste, Contribution à la commande non linéaire de systèmes d'irrigation, 2001.

G. Besançon and A. ?iclea, An Immersion-Based Observer Design for Rank-Observable Nonlinear Systems, IEEE Transactions on Automatic Control, vol.52, issue.1, pp.83-88, 2007.
DOI : 10.1109/TAC.2006.889867

F. Deza, E. Busvelle, J. P. Gauthier, and D. Rakotopara, High gain estimation for nonlinear systems, Systems & Control Letters, vol.18, issue.4, pp.295-299, 1992.
DOI : 10.1016/0167-6911(92)90059-2

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

H. Hammouri and M. Farza, Nonlinear observers for locally uniformly observable systems ESAIM : Control, optimisation and calculus of Variations, pp.353-370, 2003.

J. P. Gauthier and I. A. Kupka, Observability and Observers for Nonlinear Systems, SIAM Journal on Control and Optimization, vol.32, issue.4, pp.975-994, 1994.
DOI : 10.1137/S0363012991221791

G. Bornard, N. Couenne, and G. Gilles, Observability and observers, " in Nonlinear systems -T.1, Modeling and estimation, pp.173-216, 1995.

J. Gauthier and G. Bornard, Observability for any u(t) of a class of nonlinear systems, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pp.922-926, 1981.
DOI : 10.1109/CDC.1980.271933

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

G. Besançon and H. Hammouri, On observer design for interconnected systems, Journal of Mathematical Systems, Estimation, and Control, vol.8, issue.3, pp.1-25, 1998.

R. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.35-40, 1960.
DOI : 10.1115/1.3658902

A. Gelb, Applied optimal estimation, M.I.T., Tech. Rep, 1974.

K. Reif, F. Sonnemann, and R. Unbehauen, An EKF-Based Nonlinear Observer with a Prescribed Degree of Stability, Automatica, vol.34, issue.9, pp.1119-1123, 1998.
DOI : 10.1016/S0005-1098(98)00053-3

G. Bornard and H. Hammouri, A high gain observer for a class of uniformly observable sytems, Proc. of the 30th IIIE Conf. on Decision and Control, pp.1494-1496, 1991.

G. Bornard and H. Hammouri, A graph approach to uniform observability of nonlinear multi-output systems, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.701-706, 2002.
DOI : 10.1109/CDC.2002.1184586

J. Picard, Efficiency of the Extended Kalman Filter for Nonlinear Systems with Small Noise, SIAM Journal on Applied Mathematics, vol.51, issue.3, pp.824-885, 1991.
DOI : 10.1137/0151042

F. Deza, D. Bossanne, E. Busvelle, J. P. Gauthier, and D. Rakotopara, Exponential observers for nonlinear systems, IEEE Transactions on Automatic Control, vol.38, issue.3, pp.482-484, 1993.
DOI : 10.1109/9.210151

J. P. Gauthier and I. Kupka, Deterministic Observation theory and applications, 2001.
DOI : 10.1017/CBO9780511546648

N. Boizot, E. Busvelle, and J. P. Gauthier, An adaptive high-gain observer for nonlinear systems, Automatica, vol.46, issue.9, pp.1483-1488, 2010.
DOI : 10.1016/j.automatica.2010.06.004

E. Bullinger and F. Allgöwer, An adaptive high-gain observer for nonlinear systems, Proceedings of the 36th IEEE Conference on Decision and Control, 1997.
DOI : 10.1109/CDC.1997.649541

V. Andrieu, L. Praly, and A. Astolfi, High gain observers with updated gain and homogeneous correction terms, Automatica, vol.45, issue.2, pp.422-428, 2009.
DOI : 10.1016/j.automatica.2008.07.015

URL : https://hal.archives-ouvertes.fr/hal-00362752

J. H. Ahrens and H. K. Khalil, High-gain observers in the presence of measurement noise : A switched-gain aaproach, Automatica, vol.45, issue.4, pp.946-943, 2009.

G. Besançon, Further results on high gain observers for nonlinear systems, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), pp.2904-2909, 1999.
DOI : 10.1109/CDC.1999.831376

N. Boizot and E. Busvelle, Nonlinear observers and applications Adaptive-gain observers and applications, pp.71-114, 2007.

L. Billman and R. Isermann, Leak detection methods for pipelines, Proceeding of the 8th IFAC Congresse, pp.1813-1818, 1984.
DOI : 10.1016/0005-1098(87)90011-2

B. Brunone and M. Ferrante, Detecting leaks in pressurised pipes by means of transients, Journal of Hydraulic Research, vol.23, issue.3, pp.539-547, 2001.
DOI : 10.1080/00221686.2001.9628278

X. J. Wang, Leak Detection in Pipelines using the Damping of Fluid Transients, Journal of Hydraulic Engineering, vol.128, issue.7, pp.697-711, 2002.
DOI : 10.1061/(ASCE)0733-9429(2002)128:7(697)

W. Mpesha, M. N. Chaudry, and S. Gassman, Leak Detection in Pipes by Frequency Response Method, Journal of Hydraulic Engineering, vol.127, issue.2, pp.137-147, 2001.
DOI : 10.1061/(ASCE)0733-9429(2001)127:2(134)

D. Covas, H. Ramos, and A. B. De-almeida, Standing Wave Difference Method for Leak Detection in Pipeline Systems, Journal of Hydraulic Engineering, vol.131, issue.12, pp.1106-1116, 2005.
DOI : 10.1061/(ASCE)0733-9429(2005)131:12(1106)

M. Ferrante and B. Brunone, Pipe system diagnosis and leak detection by unsteady-state tests. 1. Harmonic analysis, Advances in Water Resources, vol.26, issue.1, pp.95-105, 2003.
DOI : 10.1016/S0309-1708(02)00101-X

C. Verde, N. Visairo, and S. Gentil, Two leaks isolation in a pipeline by transient response, Advances in Water Resources, vol.30, issue.8, pp.1711-1721, 2007.
DOI : 10.1016/j.advwatres.2007.01.001

URL : https://hal.archives-ouvertes.fr/hal-00149849

N. Bedjaoui, E. Weyer, and G. Bastin, Methods for the localization of a leak in open water channels, Networks and heterogeneous media, pp.189-210, 2009.
DOI : 10.3934/nhm.2009.4.189

E. Weyer and G. Bastin, Leak detection in open water channels, Proceedings of the 17th World Congress, 2008.
DOI : 10.3182/20080706-5-KR-1001.01337

X. J. Wang, M. F. Lambert, and A. R. Simpson, Detection and Location of a Partial Blockage in a Pipeline Using Damping of Fluid Transients, Journal of Water Resources Planning and Management, vol.131, issue.3, pp.244-249, 2005.
DOI : 10.1061/(ASCE)0733-9496(2005)131:3(244)

P. K. Mohapatra, M. H. Chaudhry, A. A. Kassem, and J. Moloo, Detection of Partial Blockage in Single Pipelines, Journal of Hydraulic Engineering, vol.132, issue.2, pp.200-206, 2006.
DOI : 10.1061/(ASCE)0733-9429(2006)132:2(200)

T. Li, Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, Discrete and Continuos Dynamical Systems, pp.243-257, 2010.
DOI : 10.3934/dcds.2010.28.243

T. Li, Observabilit?? exacte fronti??re pour des syst??mes hyperboliques quasi-lin??aires, Comptes Rendus Mathematique, vol.342, issue.12, pp.937-942, 2006.
DOI : 10.1016/j.crma.2006.02.036

C. Verde, G. Bornard, and S. Gentil, Isolability of multileaks in a pipeline, Proceedings 4th MATHMOD, 2003.

C. Verde and N. Visairo, Identificability of multi-leaks in a pipeline, Proceedings of the American Control Conference, pp.4378-4383, 2004.

O. Begovich, J. García, and B. Leon, Validation of a semiphysical pipeline model for multi-leak purposes, Proceedings of the 20th IASTED International Conference. Modelling and simulation, pp.24-29, 2009.

G. Pezzinga, Quasi-2D Model for Unsteady Flow in Pipe Networks, Journal of Hydraulic Engineering, vol.125, issue.7, pp.676-685, 1999.
DOI : 10.1061/(ASCE)0733-9429(1999)125:7(676)

E. J. Hinch, Mixing Chaos and turbulence, ch. Mixing : Turbulence and Chaos -An Introduction, pp.37-56, 1999.

O. E. Lanford, The Strange Attractor Theory of Turbulence, Annual Review of Fluid Mechanics, vol.14, issue.1, pp.347-364, 1982.
DOI : 10.1146/annurev.fl.14.010182.002023

J. P. Crutchfield, Are Attractors Relevant to Turbulence?, Physical Review Letters, vol.60, issue.26, pp.2715-2718, 1988.
DOI : 10.1103/PhysRevLett.60.2715

L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Physical Review Letters, vol.64, issue.8, pp.821-824, 1990.
DOI : 10.1103/PhysRevLett.64.821

E. Mosekilde, Y. Maistrenko, and D. Postnov, Chaotic Synchronization, Applications to living systems, World Scientific, 2002.

J. H. Park, Chaos synchronization of a chaotic system via nonlinear control, Chaos, Solitons & Fractals, vol.25, issue.3, pp.579-584, 2005.
DOI : 10.1016/j.chaos.2004.11.038

H. Nijmeijer and I. Mareels, An observer looks at synchronization, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.44, issue.10, pp.882-890, 1997.
DOI : 10.1109/81.633877

A. Loria, E. Panteley, and A. Zavala-rio, Adaptive Observers With Persistency of Excitation for Synchronization of Chaotic Systems, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.56, issue.12, pp.2703-2716, 2009.
DOI : 10.1109/TCSI.2009.2016636

G. Besançon, J. D. Leon-morales, and J. Huerta-guevara, On adaptive observers for state affine systems, International Journal of Control, vol.2, issue.6, pp.581-591, 2006.
DOI : 10.1109/9.989154

E. Lorenz, Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences, vol.20, issue.2, pp.130-141, 1963.
DOI : 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

J. Lu, X. Wu, and L. Lü, Synchronization of a unified chaotic system and the application in secure communication, Physics Letters A, vol.305, issue.6, pp.365-370, 2002.
DOI : 10.1016/S0375-9601(02)01497-4

A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952.
DOI : 10.1113/jphysiol.1952.sp004764

J. L. Hindmarsh and R. M. Rose, A model of the nerve impulse using two first-order differential equations, Nature, vol.6, issue.5853, pp.162-164, 1982.
DOI : 10.1038/296162a0

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization : A Universal Concept in Nonlinear Sciences, 2001.
DOI : 10.1017/CBO9780511755743

L. Kocarev, Z. Tasev, T. Stojanovski, and U. Parlitz, Synchronizing spatiotemporal chaos, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.7, issue.4, pp.635-643, 1997.
DOI : 10.1063/1.166263

L. Junge and U. Parlitz, Synchronization and control of coupled Ginzburg-Landau equations using local coupling, Physical Review E, vol.61, issue.4, pp.3736-3742, 2000.
DOI : 10.1103/PhysRevE.61.3736

S. Boccaletti, C. Mendoza, and J. Bragard, Synchronization of spatially extended chaotics systems with assymetric coupling, Brazilian Journal of physics, vol.35, issue.2B, pp.411-417, 2005.

S. Boccaletti, J. Bragard, and F. T. Arecchi, Controlling and synchronizing space time chaos, Physical Review E, vol.59, issue.6, pp.6574-6578, 1999.
DOI : 10.1103/PhysRevE.59.6574

G. S. Duane and J. Tribbia, Synchronized Chaos in Geophysical Fluid Dynamics, Physical Review Letters, vol.86, issue.19, pp.4298-4301, 2001.
DOI : 10.1103/PhysRevLett.86.4298

A. Khadra, X. Liu, and X. Shen, Impulsive control and synchronization of spatiotemporal chaos, Chaos, Solitons & Fractals, vol.26, issue.2, pp.615-636, 2005.
DOI : 10.1016/j.chaos.2004.01.020