On l1-gain control for 2D delayed positive systems in FM LSS models: necessary and sufficient conditions. Issue 16 (10th December 2022)

• Record Type: Journal Article
• Authors: Duan, Zhaoxia; Han, Yuchen; Xiang, Zhengrong; Ghous, Imran
• Is Part Of: International journal of systems science. Volume 53:Issue 16(2022)
• Page Start: 3449
• Page End: 3464
• Publication Date: 2022-12-10
• Subjects: Positive systems -- Fornasini-Marchesini local state-space model -- delays -- l1-gain; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2022.2090635
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : This paper presents an l 1 -gain control design for two-dimensional (2D) delayed positive systems (PSs) in the Fornasini-Marchesini local state-space model. First, for a stable 2D delayed PS, the necessary and sufficient conditions are derived for the calculation of the exact value of the l 1 -gain. Then, the controller design is given with the aid of the singular value decomposition method, which ensures that the closed-loop system is asymptotically stable at the specified l 1 -gain level. In the end, two examples are provided to identify the validity and correctness of the results of the theory.