Admissible disturbance sets for discrete perturbed systems

Jamal Bouyaghroumni; Abdelhaq El Jai; Mostafa Rachik

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 2, page 349-367
  • ISSN: 1641-876X

Abstract

top
We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated and numerical simulations are given.

How to cite

top

Bouyaghroumni, Jamal, El Jai, Abdelhaq, and Rachik, Mostafa. "Admissible disturbance sets for discrete perturbed systems." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 349-367. <http://eudml.org/doc/207510>.

@article{Bouyaghroumni2001,
abstract = {We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated and numerical simulations are given.},
author = {Bouyaghroumni, Jamal, El Jai, Abdelhaq, Rachik, Mostafa},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {bilinear disturbance; discrete systems; admissibility index; bilinear systems; discrete-time; perturbations},
language = {eng},
number = {2},
pages = {349-367},
title = {Admissible disturbance sets for discrete perturbed systems},
url = {http://eudml.org/doc/207510},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Bouyaghroumni, Jamal
AU - El Jai, Abdelhaq
AU - Rachik, Mostafa
TI - Admissible disturbance sets for discrete perturbed systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 2
SP - 349
EP - 367
AB - We consider a discrete disturbed system given by the difference bilinear equation where are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function. Let be a tolerance index on the output. The disturbance is said to be -admissible if, where is the output signal associated with the case of an uninfected system. The set of all -admissible disturbances is the admissible set. The characterization of is investigated and numerical simulations are given.
LA - eng
KW - bilinear disturbance; discrete systems; admissibility index; bilinear systems; discrete-time; perturbations
UR - http://eudml.org/doc/207510
ER -

References

top
  1. Afifi L. and ElL Jai A. (1994): Strategic sensors and spy sensors. -Appl. Math. Comp. Sci., Vol.4, No.4, pp.553-573. Zbl0823.93011
  2. Balakrishnan A.V. (1976): Applied Functional Analysis. - London: Springer. Zbl0333.93051
  3. Bensoussan A. and Viot M. (1975): Optimal control of stochastic linear distributed parameter systems. - SIAM J. Control, Vol.13, pp.904-926. Zbl0276.93058
  4. Curtain R.F. and Pritchard A.J. (1978): Infinite Dimensional Linear Systems Theory. - Berlin: Springer. Zbl0389.93001
  5. Curtain R.F. and Zwart H.J. (1995): An Introduction to Infinite-Dimensional Linear Systems Theory. -New York: Springer. Zbl0839.93001
  6. Francis D. (1987): A Course in H_∞-Control Theory. - Berlin: Springer Verlag. 
  7. Kitamura S. and Nakagiri S. (1977): Identifiability of spatially varying and constant parameters in distributed systems of parabolic type. - SIAM. J. Contr. Optim., Vol.15, No.5. Zbl0354.93020
  8. Lions J.L. (1988): Sur les sentinelles des systèmes distribues. - C.R.A.S. Paris, T.307. Zbl0664.93041
  9. Lions J.L. (1990): Furtivité et sentinelles pour les systèmes distribués à donnees in complètes. -C.R.A.S. Paris. Zbl0723.93036
  10. Rachik M., Labriji E., Abkari A. and Bouyaghroumni J. (2000): Infected discrete linear systems: On the admissible sources. -Optimization, Vol.00, pp.1-19. Zbl0978.93044
  11. Rachik M., Abdelhak A. and Karrakchou J. (1997): Discrete systems with delays in state, control and observation: The maximal output sets with state and control constraints. - Optimization, Vol.42, pp.169-183. Zbl0892.93045
  12. Suzuki T. and Murayama R. (1980): A unique theorem in an identification problem for coefficient of parabolic equations. - Proc. Japan Acad. Ser. A. Math. Sc., Vol.56, pp.259-263. Zbl0473.35076
  13. Wonham N.M. (1968): On the separation principle of stochastic control. - SIAM J. Contr., Vol.6, pp. 312-326. Zbl0164.19101
  14. Zabczyk J. (1995): Mathematical Control Theory: An Introduction, Systems and Control:Fundations and Applications. -Birkhauser. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.