Geodesic
Admissible Disturbance Sets for Discrete Perturbed Systems
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 2, pp. 349-367.

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We consider a discrete disturbed system given by the difference bilinear equation x^w_i+1 =Ax^w_i + De_i + sum_j=1^qf^j_iB_jx^w_i, i geq 0, where w=((e_i)_i geq 0, (f_i)_i geq 0) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y^w_i=Cx^w_i, i geq 0. Let varepsilon be a tolerance index on the output. The disturbance w is said to be varepsilon-admissible if ||y^w_i-y_i|| leq varepsilon, forall i geq 0, where (y_i)_i geq 0 is the output signal associated with the case of an uninfected system. The set of all varepsilon-admissible disturbances is the admissible set cal W(varepsilon). The characterization of cal W(varepsilon) is investigated and numerical simulations are given.
Keywords: discrete systems, bilinear disturbance, admissibility index
Mots-clés : system dyskretny, wskaźnik dopuszczalności 
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     title = {Admissible {Disturbance} {Sets} for {Discrete} {Perturbed} {Systems}},
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Bouyaghroumni, J.; El Jai, A.; Rachik, M. Admissible Disturbance Sets for Discrete Perturbed Systems. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 2, pp. 349-367. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_2_a2/