Problems of controllability by various totalities of Lyapunov invariants of linear differential systems in the form of $\dot x=A(t)x+B(t)u$, $x\in\mathbb R^n$, $u\in\mathbb R^m$ under the action linear closed-loop control $u=U(t)x$ are investigated. A concept of local controllability by Lyapunov exponents was proposed; sufficient conditions of this controllability were obtained. It was proved (with E. K. Makarov) a global controllability by full totality of Lyapunov invariants of two-dimensional linear systems under the condition of uniform complete controllability of the pair $(A,B)$. In the papers with E. L. Tonkov a concept of uniform consistency of linear control systems with observer was proposed; an applicability of V. M. Millionshchikov rotation method to such systems was proved.