On global controllability of the complete set of Lyapunov invariants for periodic systems

It is proved that a property of uniform complete controllability of the periodic system $\dot x=B(t)u$, $t\in\mathbb{R}$, $x\in\mathbb{R}^n$, $u\in\mathbb{R}^m$ and a property of global controllability of complete totality of Lyapunov' invariants of this system are equivalent.