C. Cassandras and S. Lafortune, Introduction to Discrete Event Systems, ser. SpringerLink Engineering, 2009.

F. Baccelli, G. Cohen, G. Olsder, and J. Quadrat, Synchronization and Linearity : An Algebra for Discrete Event Systems, 1992.

T. Brunsch, J. Raisch, and L. Hardouin, Modeling and control of highthroughput screening systems, Control Engineering Practice, vol.20, issue.1, pp.14-23, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00846116

B. Heidergott, G. Olsder, and J. Van-der-woude, Max Plus at Work: Modeling and Analysis of Synchronized Systems : a Course on Max-Plus Algebra and Its Applications, ser. Max Plus at work: modeling and analysis of synchronized systems : a course on Max-Plus algebra and its applications, p.13, 2006.

G. Cohen, S. Gaubert, and J. Quadrat, Max-plus algebra and system theory: Where we are and where to go now, Annual Reviews in Control, vol.23, pp.207-219, 1999.

M. Lhommeau, L. Hardouin, J. Ferrier, and I. Ouerghi, Interval Analysis in Dioid : Application to Robust Open Loop Control for Timed Event Graphs," in and, seville, pp.7744-7749, 2005.

M. Lhommeau, L. Hardouin, and B. Cottenceau, Optimal control for (max,+)-linear systems in the presence of disturbances, Positive Systems, Proceedings of the First Multidisciplinary International Symposium on Positive Systems: Theory and Applications, pp.47-54, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00859982

S. Amari, I. Demongodin, J. J. Loiseau, and C. Martinez, Max-plus control design for temporal constraints meeting in timed event graphs, IEEE Transactions on Automatic Control, vol.57, issue.2, pp.462-467, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00752347

V. M. Gonçalves, C. A. Maia, and L. Hardouin, On the steadystate control of timed event graphs with firing date constraints, IEEE Transactions on Automatic Control, vol.61, issue.8, pp.2187-2202, 2016.

R. D. Katz, Max-plus (A,B)-invariant spaces and control of timed discrete-event systems, IEEE Transactions on Automatic Control, vol.52, issue.2, pp.229-241, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00070485

C. A. Maia, L. Hardouin, R. Santos-mendes, and J. J. Loiseau, A supereigenvector approach to control constrained max-plus linear systems, 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp.1136-1141, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00857472

I. Necoara, B. De, T. Schutter, . Van-den, H. Boom et al., Robust control of constrained max-plus-linear systems, Int. J. of Robust and Nonlinear Control, vol.19, issue.2, pp.218-242, 2009.

M. D. Loreto, S. Gaubert, R. D. Katz, and J. Loiseau, Duality between invariant spaces for max-plus linear discrete event systems, SIAM J. on Control and Optimaztion, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00411243

L. Hardouin, C. A. Maia, B. Cottenceau, and M. Lhommeau, Observer design for (max,+) linear systems, IEEE Trans. on Automatic Control, vol.55, issue.2, pp.538-543, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00859756

D. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.596-602, 1971.

M. Diloreto, S. Gaubert, R. Katz, and J. Loiseau, Duality between invariant spaces for max-plus linear discrete event systems, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.5606-5628, 2010.

L. Hardouin, C. A. Maia, B. Cottenceau, and M. Lhommeau, Maxplus Linear Observer: Application to manufacturing Systems, pp.171-176, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00857986

B. F. Heidergott, Max-Plus Linear Stochastic Systems and Perturbation Analysis (The International Series on Discrete Event Dynamic Systems)

N. J. Secaucus and . Usa, , 2006.

G. J. Olsder, J. A. Resing, R. E. Vries, M. S. Keane, and G. Hooghiemstra, Discrete event systems with stochastic processing times, IEEE Transactions on Automatic Control, vol.35, issue.3, pp.299-302, 1990.

T. Van-den-boom and B. Schutter, Model predictive control for perturbed max-plus-linear systems, Systems & Control Letters, vol.45, issue.1, pp.21-33, 2002.

R. M. Cândido, R. Santos-mendes, L. Hardouin, and C. Maia, Particle filter for max-plus systems, 2013.

R. M. Cândido and R. S. Mendes, Filtro de partículas para sistemas max plus com densidade de importanciaÓtima, Anais do XX Congresso Brasileiro de Automática, pp.3413-3420, 2014.

D. F. Silva, R. S. Mendes, L. Hardouin, C. A. Maia, and B. Cottenceau, Filtragem estocástica aplicada a sistemas max-plus lineares, pp.1388-1393, 2011.

Q. Lu, M. Madsen, M. Milata, S. Ravn, U. Fahrenberg et al., Reachability analysis for timed automata using max-plus algebra, The Journal of Logic and Algebraic Programming, vol.81, issue.3, pp.298-313, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01087998

X. Allamigeon, S. Gaubert, and E. Goubault, Inferring min and max invariants using max-plus polyhedra, Proceedings of the 15th International Symposium on Static Analysis, ser. SAS'08, pp.189-204, 2008.

X. Allamigeon, U. Fahrenberg, S. Gaubert, R. D. Katz, and A. Legay, Tropical fouriermotzkin elimination, with an application to real-time verification, International Journal of Algebra and Computation, vol.24, issue.05, p.569607, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01087367

,

D. Adzkiya, B. D. Schutter, and A. Abate, Computational techniques for reachability analysis of max-plus-linear systems, Automatica, vol.53, issue.3, pp.293-302, 2015.

R. M. Cândido, L. Hardouin, M. Lhommeau, and R. S. Mendes, Conditional reachability of uncertain max plus linear systems, Automatica, vol.94, pp.426-435, 2018.

K. Cechlárová, Eigenvectors of interval matrices over maxplus algebra, Discrete Applied Mathematics, vol.150, issue.1, pp.2-15, 2005.

K. Cechlárová and R. Cuninghame-green, Interval systems of max-separable linear equations, Linear Algebra and its Applications, vol.340, issue.1, pp.215-224, 2002.

H. My?ková, Interval systems of max-separable linear equations, Linear Algebra and its Applications, vol.403, pp.263-272, 2005.

R. M. Cândido, L. Hardouin, M. Lhommeau, and R. S. Mendes, An algorithm to compute the inverse image of a point with respect to a nondeterministic max plus linear system, 2019.

R. E. Moore and F. Bierbaum, Methods and Applications of Interval Analysis, 1979.

T. Brunsch, L. Hardouin, C. A. Maia, and J. Raisch, Duality and interval analysis over idempotent semirings, Linear Algebra and its Applications, vol.437, pp.2436-2454, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00846169

L. Hardouin, B. Cottenceau, M. Lhommeau, and E. L. Corronc, Interval systems over idempotent semiring, Linear Algebra and its Applications, vol.431, issue.5-7, pp.855-862, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01113461

G. L. Litvinov and A. N. Sobolevski?, Idempotent interval analysis and optimization problems, Reliable Computing, vol.7, issue.5, pp.353-377, 2001.

B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter, 2004.

, the M.S degree from Universidade Estadual de Campinas (UNICAMP, Brazil, 2013) and the Ph.D. degrees from Universidade Estadual de Campinas (UNICAMP, Brazil, 2017), as well as from the University of Angers, Renato Markele Ferreira Cândido received the B.S. degree in electrical engineering from the Universidade Federal de Viosa, 2011.

, He is currently a Full Professor of Polytech Angers at the University of Angers, France. He specializes in discrete event systems, max-plus algebra, and interval analysis with applications to computer networks, manufacturing systems, Laurent Hardouin received the degrees of Master and Ph.D. in, 2004.

, He is currently an Associate Professor at the University of Angers. His main research interests include modeling and control of timed discrete event systems in max-plus algebra with applications in manufacturing systems and computer networks, Mehdi Lhommeau was born in 1975. He received the Ph.D. degree from the University of Angers, 2003.

, Currently, he is an Associate Professor in the School of Electrical and Computer Engineering, UNICAMP. His research interests include Discrete Event Dynamic Systems, Dioid Algebra, Stochastic Filtering and Modal Logic, 1981.