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.

给定具有初始状态x ₀和输出函数y _i的离散时间控制双线性系统，我们研究最大输出集 Θ(Ω) = { x ₀ ∈ ℝ ⁿ , y _i ∈ Ω, ∀ i ≥ 0} 其中 Ω 是给定的约束集，并且是 ℝ ^p的子集. 使用一些稳定性假设，我们表明 Θ(Ω) 可以通过有限数量的不等式来确定。此外，我们给出了生成集合 Θ(Ω) 的算法过程。为了说明我们的理论方法，我们提供了一些示例和数值模拟。此外，为了证明我们的方法在实际问题中的有效性，我们提供了对 SI 流行病模型和 SIR 模型的应用。