Delay-Independent stability conditions for some classes of nonlinear systems

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Delay-Independent stability conditions for some classes of nonlinear systems. / Aleksandrov, Alexander Yu; Hu, Guang Da; Zhabko, Alexey P.

In: IEEE Transactions on Automatic Control, Vol. 59, No. 8, 6708458, 08.2014, p. 2209-2214.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{524da461ccb6404388ff68ad9e5cfe34,

title = "Delay-Independent stability conditions for some classes of nonlinear systems",

abstract = "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.",

keywords = "Asymptotic stability, delay systems, large-scale systems, Lyapunov direct method, nonlinear systems",

author = "Aleksandrov, {Alexander Yu} and Hu, {Guang Da} and Zhabko, {Alexey P.}",

year = "2014",

month = aug,

doi = "10.1109/TAC.2014.2299012",

language = "English",

volume = "59",

pages = "2209--2214",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "8",

}

RIS

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