Gradient Observability for Hyperbolic System

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


The aim of this paper is to explore the concept of regional observability of the gradient for distributed hyperbolic systems evolving in spatial domain Ω and the reconstruction of the gradient of the system without the knowledge of the state. It consists in the reconstruction of the initial state gradient in a subregion ω of Ω. We give definitions and characterizations and some properties of this kind of regional observability, we also describe an approach to solve this problem, which is performed by numerical examples and simulation.
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Distributed Systems; Hyperbolic Systems; Regional Gradient Observability; Regional Reconstruction; Sensor Strategic

Full Text:



A. El Jai, A.J. Pritchard, Sensors and Actuators in Distributed Systems Analysis (Masson, 1986).

A. El Jai, M.C Simon, E. Zerrik, Regional Observability and Sensors Structures, Sensors and Actuators Journal, Vol. 39(Issue 2):95-102, November 1993.

A. El Jai and S. El Yacoubi, On the number of actuators in parabolic systems, Int. J. Appl. Math. Comput. Sci. vol.3: 673-686, 1993.

A. El Jai, M. Amouroux and E. Zerrik, Regional observability of distributed systems, International Journal of Systems Science. vol.25: 301-313,1994.

E. Zerrik and H. Bourray, Gradient observability for diffustion system, Int. J. Appl. Math. Comput. Sci. vol.13: 139-150 2003.

E. Zerrik, H. Bourray and A. Boutoulout, Regional boundary observability, numerical approach, Int. J. Appl. Math. Comput. Sci. vol.12: 143-151 2002.

E. Zerrik, H. Bourray and A. El Jai, Regional flux reconstruction for parabolic systems. International Journal of Systems Science. vol.34: 641-650 2003.

E. Zerrik, H. Bourray and S. Benhadid, Sensors and Regional observability of the wave equation. Sensors and Actuators Journal. vol.138 : 313-328, 2007.

E. Zerrik and R. Larhrissi, Regional Target Control of the wave Equation. International Journal of Systems Science. vol.32 : 233-242, 2001.

J. Bouyaghroumni, Contrôlabilité et observabilité des systèmes hyperboliques approches numériques. Thèse de Doctorat, 1990.

J. L. Lions: Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribuées, Tome 1, Contrôlabilité Exacte, Masson, Paris, 1988.

J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968.

R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Springer-Verlag, Berlin 1978.

R. F. Curtain and H. Zwart, An Introduction to Infinite Dimensional Linear Systems Theory, Texts in Applied Mathematics, Springer-Verlag, 21, New York 1995.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize