On the maximal output admissible set for a class of nonlinear discrete systems

Consider the nonlinear discrete system x(i+ 1) = A(x(i))x(i), i ≥ 0, where A is a nonlinear map such that A(x) is a real matrix for every x ∈ ℝ″, the output function is supposed to be y(i) = Cx(i), i≥0. Given a constraint set Ω ⊂ ℝ^p, an initial state x-(0) is said to be output admissible if the resulting output signal (y(i))_i satisfies the condition y(i) ∈ Ω for every integer i ≥ 0. In this paper we propose a theoretical and algorithmic studying of the set of all possible such initial states. The case of discrete delayed systems is also considered. The second part of the paper is devoted to the characterization of the output admissible initial states corresponding to a continuous-time nonlinear system with discrete output.