ICA  Vol.4 No.2 , May 2013
Domination in Controlled and Observed Distributed Parameter Systems
Abstract: We consider and we study a general concept of domination for controlled and observed distributed systems. We give characterization results and the main properties of this notion for controlled systems, with respect to an output operator. We also examine the case of actuators and sensors. Various other situations are considered and applications are given. Then, we extend this study by comparing observed systems with respect to a control operator. Finally, we study the relationship between the notion of domination and the compensation one, in the exact and weak cases.
Cite this paper: Afifi, L. , Joundi, M. , Magri, E. and Jai, A. (2013) Domination in Controlled and Observed Distributed Parameter Systems. Intelligent Control and Automation, 4, 217-226. doi: 10.4236/ica.2013.42026.

[1]   L. Afifi, A. El Jai and E. M. Magri, “Domination and Compensation in Finite Dimension Dynamical Systems,” Applied Mathematical Sciences, Vol. 4, No. 49, 2008, pp. 2443-2457.

[2]   L. Afifi, A. El Jai and E. M. Magri, “Weak and Exact Domination in Distributed Systems,” International Journal of Applied Mathematics and Computer Science, Vol. 20, No. 3, 2010, pp. 419-426. doi:10.2478/v10006-010-0031-5

[3]   L. Afifi, N. Amimi, A. El Jai and E. M. Magri, “Regional Domination in Distributed Systems,” Applied Mathematical Sciences, Vol. 6, No. 19, 2012, pp. 913-924.

[4]   A. El Jai and A. J. Pritchard, “Sensors and Actuators in Distributed Systems Analysis,” Ellis Horwood Series in Applied Mathematics, J. Wiley, 1987.

[5]   R. F. Curtain and A. J. Pritchard, “Infinite Dimensional Linear Systems Theory,” Lecture Notes in Control and Information Sciences, Vol. 8, 1978. doi:10.1007/BFb0006761

[6]   R. F. Curtain and H. J. Zwart, “An Introduction to Infinite-Dimensional Linear Systems Theory,” Texts in Applied Mathematics, Springer-Verlag, New York, 1995. doi:10.1007/978-1-4612-4224-6

[7]   L. Afifi, A. Chafiai and A. El Jai, “Regionally Efficient and Strategic Actuators,” International Journal of Systems Science, Vol. 33, No. 1, 2002, pp. 1-12. doi:10.1080/002077202317216884

[8]   L. Afifi, A. El Jai and E. Zerrik, “Systems Theory: Regional Analysis of Infinite-Dimensional Linear Systems,” Presses Universitaires de Perpignan, 2012.

[9]   A. V. Balakrishnan, “Applied Functional Analysis,” Springer Verlag, 1981.

[10]   L. Berrahmoune, “Localisation D’actionneurs pour la Controlabilité de Systèmes Paraboliques et Hyperboliques,” Application par Dualité à la Localisation de Capteurs, Thèse de 3ème Cycle, Université Mohammed V, Rabat, 1984.

[11]   J. L. Lions, “Controlabilité Exacte, Perturbations et Stabilisation des Systèmes Distributes,” Masson, Paris, 1988.