关于多维线性系统的逆

本文给出了多维线性系统求逆的新方法，与以前的方法相比，该方法将高阶矩阵的求逆转化为逐次求低阶矩阵的规范形，而且计算更简单、有效和程序化．本文进一步讨论了多维线性系统的降阶逆系统，并分别通过选取可观测空间和不可观测空间的特殊基，得到了比以往降阶逆系统的阶数更加低的降阶逆系统，揭示了原系统的可观测性对逆系统的阶的影响．

On the Inversion of Multivariable Linear Systems

A new algorithm in this paper is obtained on constructing an inverse of a multivariable linear system. Compared with the previous methods, it makes the constructing inverses of the higher order matrices into searching for the equivalent normal forms of the lower order matrices. Consequently, the calculation is more simple, efficient and programmed. Another result of the paper is that the lower reduced inverse system is obtained, by selecting a special base of the observable and non observable spaces respectively. It reveals the effect of the observability of the original systems on the order of the inverse systems.