The regulator problem is solvable for a linear dynamical system Σ \Sigma if and only if Σ \Sigma is both pole assignable and state estimable. In this case, Σ \Sigma is a canonical system (i.e., reachable and observable). When the ring R R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).

中文翻译：

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关于环和代数上的线性系统的调节器问题

当且仅当Σ\ Sigma既是极点可分配的又是状态可估计的时，线性动力学系统Σ\ Sigma的调节器问题才可解决。在这种情况下，Σ\ Sigma是一个规范系统（即，可到达且可观察）。当环RR是一个场或Noether分数的总环时，反之亦然。具有对每个规范系统都可解决调节器问题的性质的可交换环（RP环）被表征为每个可观测系统都是状态可估计的环的类（SE环），并且该类证明等于每个可达系统都是可分配极点的环的类别（PA环），规范系统的对偶也是规范环（DP环）。