On l1-gain control for 2D delayed positive systems in FM LSS models: necessary and sufficient conditions

Zhaoxia Duan, Yuchen Han, Zhengrong Xiang and Imran Ghous

International Journal of Systems Science, 2022, vol. 53, issue 16, 3449-3464

Abstract: This paper presents an $ l_{1} $ l1-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} $ l1-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} $ l1-gain level. In the end, two examples are provided to identify the validity and correctness of the results of the theory.

Date: 2022
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DOI: 10.1080/00207721.2022.2090635

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