Let \(\dot x=Ax+Bu+f(t)\) be a control system in \({\mathbb{R}}^ n\) which satisfies the Kalman condition. Under suitable hypotheses on f, the author proves that, chosen an interval \([t_ 0,t_ 1]\), for each pair \(x_ 0,x_ 1\) in \({\mathbb{R}}^ n\) there exists a constant matrix K and a constant vector v such that the solution of \(x=(A+BK)x+Bv+f(t)\), \(x(t_ 0)=x_ 0\), satisfies \(x(t_ 1)=x_ 1\).