Let \(G=NAK\) be an Iwasawa decomposition of a reductive Lie group with Lie algebra \({\mathfrak g}=\mathfrak n+a+k\) and let \(C\subseteq{\mathfrak g}\) denote a closed convex pointed cone with inner points which is invariant under the compact linear group \(\text{Ad }K\). We let \(S\) denote the closed semigroup generated in \(G\) by \(\exp C\). In general in Lie semigroup theory we say that a cone \(C\) is global in \(G\) if \(\{X\in{\mathfrak g}:\exp\mathbb{R}^ +\cdot X\subseteq S\}=C\). For a given \(C\) it is usually a delicate question to decide whether or not it is global. If \(S=G\), then \(C\) is called controllable in \(G\), whence the title. In this elegant note, the author makes the interesting discovery that globality of \(C\) can be decided by considering the Lie group \(G_ a=NA\times K\) whose Lie algebra \({\mathfrak g}_ a=\mathfrak(n+a)\oplus k\) is linearly isomorphic to \({\mathfrak g}\) in the obvious way and therefore contains a copy \(C_ a\) of \(C\). Then \(C\) is global in \(G\) iff \(C_ a\) is global in \(G_ a\). The advantage of \(G_ a\) is that the maximal subsemigroups of \(G_ a\) are known once one knows the hyperplane subalgebra of \(\mathfrak (n+a)\oplus k\). Their intersection is \(\mathfrak[n,n]\oplus[k,k]\). All of this information results in the following theorem: Assume \(G\) simply connected. If \((\text{int }C)\cap({\mathfrak n}+[\mathfrak k,k])\neq\emptyset\) then \(S=G\), i.e., \(C\) is controllable in \(G\). If \(C\cap(\mathfrak n+[k,k])=\{0\}\) then \(C\) is global in \(G\). If \(\emptyset\neq(C\cap({\mathfrak n}+[{\mathfrak k,k}]))\setminus\{0\}\subseteq\partial C\) then \(S\neq G\).