ABSTRACT

The selection of systems of inputs and outputs forms part of the early system design that is important since it preconditions the potential for control design. Existing methodologies for input, output structure selection rely on criteria expressing distance to uncontrollability, unobservability. Although controllability is invariant under state feedback, its corresponding degrees expressing distance to uncontrollability is not. The paper introduces new criteria for distance to uncontrollability (dually for unobservability) which is invariant under feedback transformations. The approach uses the restricted matrix pencils developed for the characterisation of invariant spaces of the geometric theory and then deploys exterior algebra to define the invariant input and output decoupling polynomials. This reduces the overall problem of distance to uncontrollability (unobservability) to two optimisation problems: the distance from the Grassmann variety and distance of a set of polynomials from non-coprimeness. Results on the distance of Sylvester Resultants from singularity provide the new measures.

摘要

输入和输出系统的选择构成了早期系统设计的一部分，这很重要，因为它为控制设计的潜力提供了先决条件。用于输入、输出结构选择的现有方法依赖于表示与不可控性、不可观察性的距离的标准。虽然可控性在状态反馈下是不变的，但其对应的程度表示到不可控性的距离却不是。该论文介绍了在反馈变换下保持不变的不可控性距离（双重不可观测性）的新标准。该方法使用为表征几何理论的不变空间而开发的受限矩阵铅笔，然后部署外部代数来定义不变的输入和输出解耦多项式。这将不可控性（不可观察性）距离的整体问题减少为两个优化问题：与格拉斯曼变体的距离和一组多项式与非互质性的距离。Sylvester Resultants 与奇点的距离的结果提供了新的度量。