The admissible disturbance for discrete nonlinear perturbed controlled systems

Consider the discrete perturbed controlled nonlinear system given by and the output function (x^w(i + 1) = Ax^w(i) + f(u_i + α_i) + g(v_i) Σ^r_{j = 1} β^j_ih_j (x^w(i)) i ≥ 0, x^w(0) = x₀ + γ and the output function y^w(i) = Cx^w(i), i ≥ 0, where w = (γ, (α_i)_i≥0, (β_i)_i≥0), is a disturbance which disturbs the system. The disturbance w is said to be ε-admissible if ||y^w(i) - y⁽ⁱ⁾|| ≤ e, for all i ≥ 0, where (y(i))_i≥0 is the output signal corresponding to the uninfected controlled system. The set of all ε-admissible disturbances is the admissible set E(ε). The characterization of E(ε) is investigated and practical algorithms with numerical simulations are given. The admissible set E¯(ε) for discrete delayed systems is also considered.