T. Meurer, K. Graichen, and E. Gilles, Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems, Lecture Notes in Control and Information Sciences, vol.322, issue.322, 2005.
DOI : 10.1007/11529798

H. Nijmeijer and T. I. Fossen, New Directions in Nonlinear Observer Design, 1999.
DOI : 10.1007/BFb0109917

G. Besançon, Nonlinear observers and applications, ser. Lecture Notes in Control and Inforamtion Science, 2007.

J. Tsinias, Time-varying observers for a class of nonlinear systems, Systems & Control Letters, vol.57, issue.12, pp.1037-1047, 2008.
DOI : 10.1016/j.sysconle.2008.07.001

D. Efimov, A. Zolghadri, and P. Simon, Improving fault detection abilities of extended Kalman filters by covariance matrices adjustment, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), 2010.
DOI : 10.1109/SYSTOL.2010.5676002

K. Reif and R. Unbehauen, The extended Kalman filter as an exponential observer for nonlinear systems, IEEE Transactions on Signal Processing, vol.47, issue.8, pp.2324-2328, 1999.
DOI : 10.1109/78.774779

O. Bernard and J. L. Gouzé, 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

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

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

T. Raïssi, D. Efimov, and A. Zolghadri, Interval State Estimation for a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, vol.57, issue.1, pp.260-265, 2012.
DOI : 10.1109/TAC.2011.2164820

D. Efimov, L. Fridman, T. Raïssi, A. Zolghadri, and R. Seydou, Interval estimation for LPV systems applying high order sliding mode techniques, Automatica, vol.48, issue.9, pp.2365-2371, 2012.
DOI : 10.1016/j.automatica.2012.06.073

URL : https://hal.archives-ouvertes.fr/hal-00701643

D. Efimov, T. Raïssi, and A. Zolghadri, Control of Nonlinear and LPV Systems: Interval Observer-Based Framework, IEEE Transactions on Automatic Control, vol.58, issue.3, pp.773-782, 2013.
DOI : 10.1109/TAC.2013.2241476

URL : https://hal.archives-ouvertes.fr/hal-00664106

F. Mazenc and O. Bernard, Interval observers for linear time-invariant systems with disturbances, Automatica, vol.47, issue.1, pp.140-147, 2011.
DOI : 10.1016/j.automatica.2010.10.019

URL : https://hal.archives-ouvertes.fr/hal-00555464

D. Efimov, T. Raïssi, S. Chebotarev, and A. Zolghadri, Interval state observer for nonlinear time varying systems, Automatica, vol.49, issue.1, pp.200-205, 2013.
DOI : 10.1016/j.automatica.2012.07.004

URL : https://hal.archives-ouvertes.fr/hal-00719911

L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00845131

L. Chisci, A. Garulli, and G. Zappa, Recursive state bounding by parallelotopes, Automatica, vol.32, issue.7, pp.1049-1055, 1996.
DOI : 10.1016/0005-1098(96)00048-9

E. Walter, J. Norton, H. Piet-lahanier, and M. Milanese, Bounding Approaches to System Identification, 1996.

D. G. Maksarov and J. P. Norton, Computationally efficient algorithms for state estimation with ellipsoidal approximations, International Journal of Adaptive Control and Signal Processing, vol.38, issue.6, pp.411-434, 2002.
DOI : 10.1002/acs.696

B. T. Polyak, S. A. Nazin, C. Durieu, and E. Walter, Ellipsoidal parameter or state estimation under model uncertainty, Automatica, vol.40, issue.7, pp.1171-1179, 2004.
DOI : 10.1016/j.automatica.2004.02.014

T. Alamo, J. M. Bravo, and E. F. Camacho, Guaranteed state estimation by zonotopes, Automatica, vol.41, issue.6, pp.1035-1043, 2005.
DOI : 10.1016/j.automatica.2004.12.008

URL : https://hal.archives-ouvertes.fr/hal-00708563

D. Efimov, W. Perruquetti, T. Raïssi, and A. Zolghadri, On interval observer design for discrete systems, Proc. ECC 2013, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00801806

F. Mazenc, T. N. Dinh, and S. I. Niculescu, Interval observers for discrete-time systems, Proc. IEEE CDC 2012, pp.6755-6760, 2012.
DOI : 10.1002/rnc.3030

URL : https://hal.archives-ouvertes.fr/hal-00761600

M. W. Hirsch and H. L. Smith, Monotone maps: a review, Journal of Difference Equations and Applications, vol.21, issue.4-5, pp.379-398, 2005.
DOI : 10.1017/S0004972700017032

R. H. Bartels and G. W. Stewart, Solution of the matrix equation AX + XB = C [F4], Communications of the ACM, vol.15, issue.9, pp.820-826, 1972.
DOI : 10.1145/361573.361582

A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences, ser. Classics in applied mathmatics, 1994.

O. Rojo and H. Rojo, Constructing symmetric nonnegative matrices via the fast fourier transform, Computers & Mathematics with Applications, vol.45, issue.10-11, pp.1655-1672, 2003.
DOI : 10.1016/S0898-1221(03)00145-7

A. Khalanai and D. Veksler, Qualitative Theory of Sampled-Data Systems, 1971.

S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, ser. Communications and Control Engineering, 2008.

I. V. Gaishun, The canonical form of reducible discrete systems with degenerate coefficient matrices, Differential Equations, vol.11, issue.6, pp.1043-1049, 2000.
DOI : 10.1007/BF02754506

G. Millerioux, L. Rosier, G. Bloch, and J. Daafouz, Bounded State Reconstruction Error for LPV Systems With Estimated Parameters, IEEE Transactions on Automatic Control, vol.49, issue.8, pp.1385-1389, 2004.
DOI : 10.1109/TAC.2004.832669

URL : https://hal.archives-ouvertes.fr/hal-00121005

W. Heemels, J. Daafouz, and G. Millerioux, Observer-Based Control of Discrete-Time LPV Systems With Uncertain Parameters <formula formulatype="inline"> <tex Notation="TeX">$ $</tex></formula>, IEEE Transactions on Automatic Control, vol.55, issue.9, pp.2130-2135, 2010.
DOI : 10.1109/TAC.2010.2051072

I. Konstantopoulos and P. Antsaklis, New bounds for robust stability of continuous and discrete-time systems under parametric uncertainty, Kybernetika, vol.31, issue.6, pp.623-636, 1995.

M. B. Elowitz and S. Leibler, A synthetic oscillatory network of transcriptional regulators, Nature, vol.403, issue.6767, pp.335-338, 2000.
DOI : 10.1038/35002125

G. Lillacci and M. Khammash, Parameter Estimation and Model Selection in Computational Biology, PLoS Computational Biology, vol.403, issue.3, p.1000696, 2010.
DOI : 10.1371/journal.pcbi.1000696.s002