On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems

Given a discrete-time controlled bilinear systems with initial state x₀ and output function y_i, we investigate the maximal output set Θ(Ω) = {x₀ ∈ ℝⁿ, y_i ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ^p. Using some stability hypothesis, we show that Θ(Ω) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Θ(Ω). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model.