Benfatah Y, El Bhih A, Rachik M, Tridane A. On the Maximal Output Admissible Set for a Class of Bilinear
Discrete-time Systems.
Int J Control Autom Syst 2021;
19:3551-3568. [PMID:
34493935 PMCID:
PMC8412393 DOI:
10.1007/s12555-020-0486-6]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Revised: 01/06/2021] [Accepted: 01/31/2021] [Indexed: 06/13/2023]
Abstract
Given a discrete-time controlled bilinear systems with initial state x 0 and output function y i , we investigate the maximal output set Θ(Ω) = {x 0 ∈ ℝ n , 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.
Collapse