论文标题
$ \ mathrm {sl} \ left（n，\ mathbb {h} \ right）$在$ \ mathrm {sl} \ left上的不变控制系统的可控性和可控性
Semigroups and Controllability of Invariant Control Systems on $\mathrm{Sl}\left(n,\mathbb{H}\right)$
论文作者
论文摘要
令$ \ mathrm {sl} \ left（n，\ mathbb {h} \ right）$是$ n \ times n $ quaternionic矩阵$ g $的谎言组，带有$ \ left \ welet \ vert \ vert \ det g \ det g \ right \ right \ right \ vert = 1 $。我们证明，具有非空内部的subigroup $ s \ subset \ subset \ mathrm {sl} \ left（n，\ mathbb {h} \ right）$等于$ \ mathrm {slrm {sl} \ left（n，n，\ mathbb {h} 2，\ mathbb {h} \ right）$。作为应用程序，我们在$ a，b \ in \ mathfrak {sl} \ left（n，\ mathbb {h} \ right）上提供足够的条件，以确保不变的控制系统$ \ dot {g} = ag+ag+ubg $在$ \ mathrm {sl} \ weft（n，n，n，n，n，n，sl n，n，n，sl n，n，n，sl n，n，n，sl sl sl} \ left $ \ mathrm {slrm {slrm {slrm {slrm {我们还证明，这些条件是通用的，从某种意义上说，我们获得了一组开放而密集的可控对$ \ left（a，b \ right）\ in \ mathfrak {sl} \ left（n，\ mathbb {h} \ right）^{2} $。
Let $\mathrm{Sl}\left( n,\mathbb{H}\right)$ be the Lie group of $n\times n$ quaternionic matrices $g$ with $\left\vert \det g\right\vert =1$. We prove that a subsemigroup $S \subset \mathrm{Sl}\left( n,\mathbb{H}\right)$ with nonempty interior is equal to $\mathrm{Sl}\left( n,\mathbb{H}\right)$ if $S$ contains a subgroup isomorphic to $\mathrm{Sl}\left( 2,\mathbb{H}\right)$. As application we give sufficient conditions on $A,B\in \mathfrak{sl}\left( n,\mathbb{H}\right)$ to ensuring that the invariant control system $\dot{g}=Ag+uBg$ is controllable on $\mathrm{Sl}\left( n,\mathbb{H}\right)$. We prove also that these conditions are generic in the sense that we obtain an open and dense set of controllable pairs $\left( A,B\right)\in\mathfrak{sl}\left( n,\mathbb{H}\right)^{2}$.
