Admissible Disturbance Sets for Discrete Perturbed Systems

We consider a discrete disturbed system given by the difference bilinear equation x^{w}_{i+1} =Ax^{w}_{i} + De_{i} + sum_{j=1}^{q}f^{j}_{i}B_{j}x^{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.