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A New Approach to the Internally Positive Representation of Linear MIMO Systems

机译：线性MIMO系统内部正表示的一种新方法。

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摘要

The problem of representing linear systems through combination of positive systems is relevant when signal processing schemes, such as filters, state observers, or control laws, are to be implemented using “positive” technologies, such as Charge Routing Networks and fiber optic filters. This problem, well investigated in the SISO case, can be recasted into the more general problem of Internally Positive Representation (IPR) of systems. This paper presents a methodology for the construction of such IPRs for MIMO systems, based on a suitable convex positive representation of complex vectors and matrices. The stability properties of the IPRs are investigated in depth, achieving the important result that any stable system admits a stable IPR of finite dimension. A main algorithm and three variants, all based on the proposed methodology, are presented for the construction of stable IPRs. All of them are straightforward and are characterized by a very low computational cost. The first and second may require a large state-space dimension to provide a stable IPR, while the third and the fourth are aimed to provide stable IPRs of reduced order.
机译：当要使用诸如电荷路由网络和光纤滤波器之类的“正”技术来实现诸如滤波器，状态观测器或控制律之类的信号处理方案时，通过正系统的组合来表示线性系统的问题就显得尤为重要。在SISO案例中对此问题进行了深入研究，可以将其重铸为系统内部正表示（IPR）的更一般问题。本文提出了一种基于复杂矢量和矩阵的凸正表示形式的MIMO系统IPR构造方法。深入研究了IPR的稳定性，取得了重要结果，即任何稳定的系统都可以接受有限尺寸的稳定IPR。提出了主要算法和三个变体，它们均基于所提出的方法，用于构建稳定的IPR。它们都很简单，并且具有非常低的计算成本。第一和第二个可能需要较大的状态空间维度以提供稳定的IPR，而第三个和第四个旨在提供降序的稳定IPR。

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