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

Youssef Benfatah, Amine El Bhih, Mostafa Rachik, and Abdessamad Tridane*
International Journal of Control, Automation, and Systems, vol. 19, no. 11, pp.3551-3568, 2021

Abstract : Given a discrete-time controlled bilinear systems with initial state x0 and output function yi, we investigate the maximal output set Θ(Ω) = {x0 ∈ Rn, yi ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of Rp. 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.

Keyword : Asymptotic stability, bilinear systems, constraint set, discrete-time systems, output admissible set.

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