Geodesic
A control procedure for total set of Lyapunov invariants for linear systems in nondegenerate case
Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 33-37

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Let the differential system $\dot{x}=(A(t)+B(t)U(t))x$, $x\in\mathbb{R}^n$, $t\ge 0$ has bounded piecewise continuous square coefficient matrices $A$ and $B$ and let the control matrix $U$ be of the same type. It is proved that the total Lyapunov invariants set of this system is globolly controllable if there exist numbers $\sigma>0$ and $\alpha>0$ such that the inequality $\int_{t_0}^{t_0+\sigma}|{\det B(\tau)}|\,d\tau\ge\alpha$ holds for all $t_0\ge 0$. 
@article{TIMB_2007_15_2_a3,
     author = {A. A. Kozlov},
     title = {A control procedure for total set of {Lyapunov} invariants for linear systems in nondegenerate case},
     journal = {Trudy Instituta matematiki},
     pages = {33--37},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2007_15_2_a3/}
}
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A. A. Kozlov. A control procedure for total set of Lyapunov invariants for linear systems in nondegenerate case. Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 33-37. http://geodesic.mathdoc.fr/item/TIMB_2007_15_2_a3/