This paper is devoted to the analysis of the ℓ₁-induced norm and proposes a novel characterization for 2-D positive systems. As we know that the most popular models of 2-D linear systems were introduced by Roesser, Fornasini and Marchesini. For those two models, an analytical method to compute the exact value of ℓ₁-induced norm is first presented. Then, on the basis of these results, a novel characterization for stability and ℓ₁-induced performance is proposed for 2-D positive systems. Those characterization are formulated in the form of linear programming (LP). Finally, the theoretical results are illustrated through a numerical example.

中文翻译：

---

ℓ ₁诱导的范数和表征合成2- d正系统

本文专门ℓ的分析₁诱导的范数，并提出了2-d正系统的新颖特征。众所周知，Roesser，Fornasini和Marchesini引入了最流行的二维线性系统模型。对于这两个模型，首先提出了一种计算method ₁诱导范数精确值的分析方法。然后，这些结果的基础上，用于稳定和ℓ一种新颖的表征_1和诱导的性能提出了2-d阳性系统。这些特征以线性编程（LP）的形式表示。最后，通过数值例子说明了理论结果。