This paper is motivated by the asymptotic stabilization of abstract SPDEs of linear type. As a first step, it proposes an abstract contribution to the exact controllability (in a general ${\mathbb{L}}^p$-sense, $p>1$) of a class of linear SDEs with general time-invariant rank control coefficient in the diffusion term. From this point of view, our paper generalizes some of the results in Wang et al. (2017) where full and null rank were considered. Necessary conditions and sufficient ones are discussed and their hierarchy and connections with the approximate controllability are illustrated. Second, our paper illustrates, on relevant frameworks of linear SPDEs, a way to drive exactly to 0 their unstable part of dimension $n\ge 1$ by using $M$ internal, respectively $N$ boundary controls such that $max\left\{M,N\right\}<n$. Extensive examples are presented as is the minimal gain for judicious control pairs.

本文的动机是线性类型的抽象 SPDE 的渐近稳定。作为第一步，它提出了对精确可控性的抽象贡献（一般来说${\mathbb{升}}^{磷}$-感觉， $磷>1$) 是一类在扩散项中具有一般时不变秩控制系数的线性 SDE。从这个角度来看，我们的论文概括了 Wang 等人的一些结果。（2017 年），其中考虑了完整排名和空排名。讨论了必要条件和充分条件，并说明了它们的层次和与近似可控性的联系。其次，我们的论文在线性 SPDE 的相关框架上说明了一种将维的不稳定部分精确驱动到 0 的方法$n\ge 1$ 通过使用 $米$ 内部，分别 $N$ 边界控制使得 $最大限度\left\{米,N\right\}<n$. 提供了大量示例以及明智控制对的最小增益。