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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $t_0\ge 0$. 
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     title = {A control procedure for total set of {Lyapunov} invariants for linear systems in nondegenerate case},
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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/

[1] Makarov E.K., Popova S.N., “O globalnoi upravlyaemosti polnoi sovokupnosti lyapunovskikh invariantov dvumernykh lineinykh sistem”, Differents. uravneniya, 35:1 (1999), 97–106 | MR | Zbl

[2] Demidovich B.P., Lektsii po matematicheskoi teorii ustoichivosti, Izd-vo Mosk. un-ta, M., 1998 | MR

[3] Kozlov A.A., Makarov E.K., “O ravnomernoi globalnoi dostizhimosti lineinykh upravlyaemykh sistem v nevyrozhdennom sluchae”, Vesnik VDU, 2007, no. 3(45), 100–109

[4] Kozlov A.A., Makarov E.K., “Ob upravlenii pokazatelyami Lyapunova lineinykh sistem v nevyrozhdennom sluchae”, Differents. uravneniya, 43:5 (2007), 621–627 | MR | Zbl

[5] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[6] Makarov E.K., “O diskretnosti asimptoticheskikh invariantov lineinykh differentsialnykh sistem”, Differents. uravneniya, 34:10 (1998), 1322–1331 | MR | Zbl