Discrete nonlinear systems: on the admissible nonlinear disturbances

Let us consider a discrete distributed system given by the difference equat ion {x(i+1)(xi) = Ax(i)(xi) + Be-i + g(beta (i)) f(x(i)(xi)), For Alli greater than or equal to0, {x(0)(xi) = x(0) + w, where xi = (w, (ei)(i greater than or equal to0), (beta (i))(i greater than or equal to0)) is a disturbance which excites the system. We assume that t he system is augmented with the output function y(i)(xi) = Cx(i)(xi), For A lli greater than or equal to0. Let epsilon be a tolerance index, we say tha t a disturbance xi is epsilon -admissible if parallel toy(i)(xi) - y(i)para llel to less than or equal to epsilon, For Alli greater than or equal to0, where (y(i))(i greater than or equal to0) is the output signal associated t o the uninfected system. The set of all epsilon -admissible disturbances is the admissible set D(epsilon). The characterization of D(epsilon) is inves tigated and numerical simulations are given. The case of discrete delayed s ystems is also considered. (C) 2001 The Franklin Institute. Published by El sevier Science Ltd. All rights reserved.