In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent singular and non-singular 2-D state space representations. Particularly, a zero coprime system equivalence transformation resulting in a singular Roesser state space model, preserving the core algebraic structure of the original system matrix, is proposed. As a second step utilizing the singular Roesser model introduced, we further reduce the system to a non-singular, zero coprime system equivalent Roesser model. Both models are constructed by inspection or by applying elementary matrix manipulations and have significantly smaller dimensions compared to similar reductions found in the literature.

中文翻译：

---

关于将重复过程简化为奇异和非奇异 Roesser 模型

在本文中，我们提出了将描述离散线性重复过程的多项式系统矩阵简化为等效奇异和非奇异二维状态空间表示的新方法。特别地，提出了一种零互素系统等价变换，产生了一个奇异的 Roesser 状态空间模型，保留了原始系统矩阵的核心代数结构。作为利用引入的奇异 Roesser 模型的第二步，我们进一步将系统简化为非奇异、零互质系统等效 Roesser 模型。这两个模型都是通过检查或应用基本矩阵操作构建的，与文献中发现的类似减少相比，它们的维度要小得多。