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

This paper presents an 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 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 𝑙1-gain level. In the end, two examples are provided to identify the validity and correctness of the results of the theory.