Protector control: Extension to a class of nonlinear distributed systems

Afifi, L., Chafiai, A. and El Jai, A. (2002). Regionally efficient and strategic actuators, International Journal of Systems Science 33(4): 1-12.10.1080/002077202317216884Search in Google Scholar

Afifi, L., El Jai, A. and Merry, M. (2000). Detection and sources reconstruction in a tube, International Journal of Systems Science 31(2): 149-159.10.1080/002077200291262Search in Google Scholar

Afifi, L., El Jai, A. and Merry, M. (2001). Regional detection and reconstruction of unknown internal or boundary sources, International Journal of Applied Mathematics and Computer Science 11(2): 319-348.Search in Google Scholar

Beltrami, E. (1987). Mathematics for Dynamic Modelling, Academic Press, San Diego, CA.10.1016/B978-0-12-085555-1.50005-3Search in Google Scholar

Bernoussi, A. (2007). Spreadability and vulnerability of distributed parameter systems, International Journal of Systems Science 38(4): 305-317.10.1080/00207720601159787Search in Google Scholar

Bernoussi, A. and Amharref, M. (2003). Etalabilité—vulnrabilité, Annals of University of Craiova, Mathematics and Computer Science Series 30(4): 53-62.Search in Google Scholar

Bernoussi, A. and El Jai, A. (2000). New approach of spreadability, Journal of Mathematical and Computer Modelling 31(13): 93-109.10.1016/S0895-7177(00)00114-XSearch in Google Scholar

Bernoussi, A., El Jai, A. and Pritchard, A. J. (2001). Spreadability and evolving interfaces, International Journal of Systems Science 32(10): 1217-1232.10.1080/00207720110035246Search in Google Scholar

Bernoussi, A. (2010). Spreadability, vulnerability and protector control, Mathematical Modelling of Natural Phenomena 5(7): 145-150, DOI: 10.1051/mmnp/20105724.10.1051/mmnp/20105724Search in Google Scholar

Curtain, R. F. and Pritchard, A. J. (1978). Infinite Dimensional Linear Systems Theory, Springer, Berlin.10.1007/BFb0006761Search in Google Scholar

Dautray, R. F. and Lions, J. (1984). Analyse mathématique et calcul numérique pour les sciences et les techniques, Série Scientifique, Tome 3, Masson, Paris.Search in Google Scholar

Diaz, J. I. and Lions, J. L. (1993). Mathematics Climate and Environment, Research in Applied Mathematics, RMA 27, Masson, Paris.Search in Google Scholar

El Jai, A. (2002). Analyse régionale des systémes distribuès, SMAI (Société de Mathématiques Appliquées et Industrielles), ESAIM—European Series in Applied and Industrial Mathematics 8: 663-692.10.1051/cocv:2002054Search in Google Scholar

El Jai, A. (2004). Eléments d'Analyse et Contrôle des Systèmes, Collection études, University of Perpignan Press, Perpignan.Search in Google Scholar

El Jai, A. and Kassara, K. (1994). Spreadable distributed systems, Mathematical and Computer Modelling 20(1): 47-64.10.1016/0895-7177(94)90218-6Search in Google Scholar

El Jai, A. and Kassara, K. (1996). Spreadability of transport systems, International Journal of Systems Science 27(7): 681-688.10.1080/00207729608929265Search in Google Scholar

El Jai, A. and Pritchard, A. J. (1986). Capteurs et actionneurs dans l'analyse des systems distribués, RMA 3, Masson, Paris.Search in Google Scholar

El Jai, A., Simon, M., Zerrik, E. and Pritchard, A. J. (1995). Regional controllability of distributed systems, International Journal of Control 62(6): 1351-1365.10.1080/00207179508921603Search in Google Scholar

Giuggioli, L. and Kenkre, V. M. (2003). Analytic solutions of a nonlinear convective equation in population dynamics, Physica D 183: 245-259.10.1016/S0167-2789(03)00176-3Search in Google Scholar

Henry, D. (1981). Geometric Theory of Semilinear Parabolic Systems, Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin/New York, NY.Search in Google Scholar

Ichikawa, A. (1982). Quadratic control of evolution equations with delays in control, SIAM Journal Control and Optimization 20(5): 645-668.10.1137/0320048Search in Google Scholar

Kenkre, V. M. (2004). Results from variants of the Fisher equation in the study of epidemics and bacteria, Physica A 342: 242-248.10.1016/j.physa.2004.04.084Search in Google Scholar

Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag, New York, NY, Berlin/Heidelberg/Tokyo.Search in Google Scholar

Qaraai, Y. (2008). Compensation des perturbations étalables et contrôle protecteur des zones vulnrables, Ph.D. thesis, Faculty of Sciences and Techniques of Tangier, Morocco.Search in Google Scholar

Qaraai, Y., Bernoussi, A. and El Jai, A. (2006). Contrôle protecteur et remdiabilité, Proceeding of the 3rd International Congress on Scientific Advances in Civil and Industrial Engineering, Algeciras, Spain, pp. 108-114.Search in Google Scholar

Qaraai, Y., Bernoussi, A. and El Jai, A. (2008). How to compensate a spreading disturbance for a class of nonlinear systems, International Journal Applied Mathematics and Computer Science 18(2): 171-187, DOI: 10.2478/v10006-008-0016-9.10.2478/v10006-008-0016-9Search in Google Scholar

Qaraai, Y., Bernoussi, A. and El Jai, A. (2009). Protector control for a class of nonlinear systems, Proceeding of the International Conference on Systems Theory: Modeling, Analysis and Control, Fes2009, Fes, Morocco, pp. 265-272.Search in Google Scholar

Smart, D. R. (1994). Fixed Point Theorems, Cambridge University Press, London.Search in Google Scholar

Zerrik, E., El Jai, A. and Amouroux, M. (1994). Regional observability of distributed systems, International Journal of Systems Science 25(6): 301-313.10.1080/00207729408928961Search in Google Scholar