On Razumikhin approach for partial stability problem of retarded systems / Vorotnikov V.I. // Applied Mathematical Sciences. - 2015. - V. 9, l. 121. - P. 6021-6028.

ISSN:
1312885X
Type:
Article
Abstract:
For nonlinear retarded functional differential systems the problem of asymptotic stability with respect to a part of the variables of a "partial" equilibrium position is considered. The condition of uniform asymptotic stability of this type is obtained in the context of the Razumikhin approach. © 2015 V.I. Vorotnikov.
Author keywords:
Nonlinear retarded functional differential systems; Partial uniform asymptotic stability; Razumikhin approach
Index keywords:
нет данных
DOI:
10.12988/ams.2015.58511
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84981156869&doi=10.12988%2fams.2015.58511&partnerID=40&md5=50da6b02feed2f6fd8d27a1292dcb757
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84981156869&doi=10.12988%2fams.2015.58511&partnerID=40&md5=50da6b02feed2f6fd8d27a1292dcb757
Affiliations Ural Federal University, Ul. Mira, 19, Ekaterinburg, Russian Federation
Author Keywords Nonlinear retarded functional differential systems; Partial uniform asymptotic stability; Razumikhin approach
References Vorotnikov, V.I., Partial stability and control: the state of the art and developing prospects (2005) Autom. Remote Control, 66, pp. 511-561. , http://dx.doi.org/10.1007/s10513-005-0099-9; Vorotnikov, V.I., (1998) Partial Stability and Control, , Birkhauser, Boston; Vorotnikov, V.I., Martyshenko, Y.G., On the partial stability of nonlinear dynamical systems (2010) J. Comput. Syst. Sci. Int, 49, pp. 702-709. , http://dx.doi.org/10.1134/S1064230710050047; Razumikhin, B.S., On stability of systems with delay (1956) Prikl. Mat. Mekh, 20, pp. 500-512. , (in Russian); Krasovskii, N.N., On asymptotic stability of retarded systems (1956) Prikl. Mat. Mekh, 20, pp. 513-518. , (in Russian); Krasovskii, N.N., (1963) On Stability of Motion, , Stanford University Press, Stanford; Razumikhin, B.S., (1988) The Stability of Hereditary Systems, , Nauka, Moscow. (in Russian); Vorotnikov, V.I., Martyshenko, Y.G., Stability in a part of variables of "partial" equilibria of systems with aftereffect (2014) Mathematical Notes, 96, pp. 477-483. , http://dx.doi.org/10.1134/s0001434614090223; Vorotnikov, V.I., On partial stability of retarded functional differential systems (2015) Applied Mathematical Sciences, 9, pp. 279-284. , http://dx.doi.org/10.12988/ams.2015.411905; Vorotnikov, V.I., On uniform partial asymptotic stability of retarded functional differential systems (2015) Applied Mathematical Sciences, 9, pp. 4149-4154. , http://dx.doi.org/10.12988/ams.2015.55375; Hale, J., (1977) Theory of Functional Differential Equations. Springer-Verlag, , http://dx.doi.org/10.1007/978-1-4612-9892-2, New York; Burton, T.A., (1985) Stability and Periodic Solutions of Ordinary and Functional Differential Equations, , Academic Press, Orlando; Bernfeld, S.R., Corduneanu, C., Ignatyev, A.O., On the stability of invariant sets of functional differential equations (2003) Nonlinear Anal., Theory Methods Appl, 55, pp. 641-656. , http://dx.doi.org/10.1016/j.na.2003.08.002; Vorotnikov, V.I., Problems of stability with respect to part of the variables (1999) J. Appl. Math. Mech, 63, pp. 695-703. , http://dx.doi.org/10.1016/S0021-8928(99)00088-X
Correspondence Address Vorotnikov, V.I.; Ural Federal University, Ul. Mira, 19, Russian Federation
Publisher Hikari Ltd.
Language of Original Document English
Abbreviated Source Title Appl. Math. Sci.
Source Scopus