On the ℓ_∞-gain of 2D positive Roesser systems with bounded time-varying delays

The focus of this article is on ℓ_∞-gain analysis and the observer design, which are applicable to linear two-dimensional (2D) positive systems (PSs) featuring bounded time-varying delays. Firstly, a computation method for the exact ℓ_∞-gain value of linear 2D PSs with no delay and constant delays is presented. Secondly, by constructing the comparison results with the constant delayed systems, it is found that the ℓ_∞-gain of the addressed system is exactly that of a constant delayed system where the constant delay is the upper bound of the time-varying delays. To maintain the asymptotic stability and optimal ℓ_∞-gain performance, necessary and sufficient conditions in the form of Linear Programming (LP) are created. Thirdly, a positive observer is further designed to ensure that the residual system remains asymptotically stable and has the optimal ℓ_∞-gain performance, but only an algorithm for obtaining a sufficient solution is given. Finally, two examples are given to show that the above findings are correct.