TY - JOUR
T1 - On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
AU - Benfatah, Youssef
AU - El Bhih, Amine
AU - Rachik, Mostafa
AU - Tridane, Abdessamad
N1 - Funding Information:
The authors would like to thank the reviewer for his time to help improve this paper. Research reported in this paper was supported by the Moroccan Systems Theory Network.
Publisher Copyright:
© 2021, ICROS, KIEE and Springer.
PY - 2021/11
Y1 - 2021/11
N2 - 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.
AB - 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.
KW - Asymptotic stability
KW - bilinear systems
KW - constraint set
KW - discrete-time systems
KW - output admissible set
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U2 - 10.1007/s12555-020-0486-6
DO - 10.1007/s12555-020-0486-6
M3 - Article
AN - SCOPUS:85114104234
VL - 19
SP - 3551
EP - 3568
JO - International Journal of Control, Automation and Systems
JF - International Journal of Control, Automation and Systems
SN - 1598-6446
IS - 11
ER -