Discrete nonlinear systems: on the admissible nonlinear disturbances

Let us consider a discrete distributed system given by the difference equationxi+1ξ=Axiξ+Bei+g(βi) f(xiξ), ∀i⩾0,x0ξ=x0+w,where ξ=(w,(ei)i⩾0,(βi)i⩾0) is a disturbance which excites the system. We assume that the system is augmented with the output function yiξ=Cxiξ, ∀i⩾0. Let ε be a tolerance index, we say that a disturbance ξ is ε-admissible if ||yiξ−yi||⩽ε, ∀i⩾0, where (yi)i⩾0 is the output signal associated to the uninfected system. The set of all ε-admissible disturbances is the admissible set D(ε). The characterization of D(ε) is investigated and numerical simulations are given. The case of discrete delayed systems is also considered.