This paper studies the action of the feedback group F(n,m) on m-input, n-dimensional reachable linear dynamical systems over a principal ideal domain R. For such a 2-dimensional system sigma a complete set of invariants is given which characterizes the feedback class of sigma. In particular it is characterized, in terms of these invariants, when sigma has the feedback cyclization property. The particular cases R = Z and R = R[X] are studied in some detail. Finally, when n is arbitrary, the feedback classification is given for the class of reachable systems sigma = (F,G) such that G is a matrix with at least n - 1 invariant factors equal to one. [References: 9]
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机译：本文研究了反馈组F（n，m）在主要理想域R上的m个输入，n维可到达线性动力学系统上的作用。对于这样的二维系统sigma，给出了完整的不变量集表征sigma的反馈类别。特别地，就这些不变量而言，其特征在于σ具有反馈环化特性。详细研究了R = Z和R = R [X]的特殊情况。最后，当n为任意时，针对可到达系统的类别sigma =（F，G）给出反馈分类，以使G为矩阵，其中n-1个不变因子至少等于1。 [参考：9]
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