Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
18 January 2020 |
02 February 2020 |
10 March 2020 |
Abstract: Consider the semilinear system defined byx (i+1) = Ax(i)+ f (x (i)) , i ≥0x (0)=x₀ ∈ ℝⁿ and the corresponding output signal y(i) =Cx(i), i ≥0, where A is a nn matrix, C is a pxn matrix and f is a nonlinear function. An initial state x₀ is output admissible with respect to A, f , C and a constraint set Ω⊂ ℝ^{p}, if the output signal (y(i))i associated to our system satisfies the condition y(i) ∈ Ω, for every integer i ≥0. The set of all possible such initial conditions is the maximal output admissible set Γ(Ω). In this paper we will define a new set that characterizes the maximal output set in various systems (controlled and uncontrolled systems). Therefore, we propose an algorithmic approach that permits to verify if such set is finitely determined or not. The case of discrete delayed systems is taken into consideration as well. To illustrate our work, we give various numerical simulations.
