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Delay-Independent stability conditions for some classes of nonlinear systems. / Aleksandrov, Alexander Yu; Hu, Guang Da; Zhabko, Alexey P.
в: IEEE Transactions on Automatic Control, Том 59, № 8, 6708458, 08.2014, стр. 2209-2214.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Delay-Independent stability conditions for some classes of nonlinear systems
AU - Aleksandrov, Alexander Yu
AU - Hu, Guang Da
AU - Zhabko, Alexey P.
PY - 2014/8
Y1 - 2014/8
N2 - Some classes of nonlinear time-delay systems are studied. It is assumed that the zero solution of a system is asymptotically stable when delay is equal to zero. By the Lyapunov direct method, and the Razumikhin approach, it is shown that in the case when the system is essentially nonlinear, i.e., the right-hand side of the system does not contain linear terms, the asymptotic stability of the trivial solution is preserved for an arbitrary positive value of the delay. Based on homogeneous approximation of a time-delay system some stability conditions are found. We treat large-scale systems with nonlinear subsystems. New stability conditions in certain cases, critical in the Lyapunov sense, are obtained. Three examples are given to demonstrate effectiveness of the presented results.
AB - Some classes of nonlinear time-delay systems are studied. It is assumed that the zero solution of a system is asymptotically stable when delay is equal to zero. By the Lyapunov direct method, and the Razumikhin approach, it is shown that in the case when the system is essentially nonlinear, i.e., the right-hand side of the system does not contain linear terms, the asymptotic stability of the trivial solution is preserved for an arbitrary positive value of the delay. Based on homogeneous approximation of a time-delay system some stability conditions are found. We treat large-scale systems with nonlinear subsystems. New stability conditions in certain cases, critical in the Lyapunov sense, are obtained. Three examples are given to demonstrate effectiveness of the presented results.
KW - Asymptotic stability
KW - delay systems
KW - large-scale systems
KW - Lyapunov direct method
KW - nonlinear systems
UR - http://www.scopus.com/inward/record.url?scp=84905272907&partnerID=8YFLogxK
U2 - 10.1109/TAC.2014.2299012
DO - 10.1109/TAC.2014.2299012
M3 - Article
VL - 59
SP - 2209
EP - 2214
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 8
M1 - 6708458
ER -
ID: 7028320