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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 4, Pages 851–862 (Mi smj2576)  
Lyapunov's direct method for linear systems of functional-differential equations in Sobolev space

R. K. Romanovsky, E. M. Nazaruk

Omsk State Technical University, Omsk, Russia
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Abstract: We establish a criterion for exponential stability in the $\mathrm H^1$-topology in terms of operator inequalities for a linear FDE system of retarded type by Lyapunov's direct method. As a corollary, some sufficient condition of exponential stability in terms of the matrix specifying the Stieltjes integral is obtained in the autonomous case. A few examples illustrating the results are exhibited.
Keywords: reduction to a difference equation in a Sobolev space, matrix realization of operators in $\mathrm H^1(0,1)$, stability in $\mathrm H^1$-topology, Lyapunov functional.
Received: 17.11.2012
Revised: 30.03.2014
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 4, Pages 696–705
DOI: https://doi.org/10.1134/S0037446614040119
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: R. K. Romanovsky, E. M. Nazaruk, “Lyapunov's direct method for linear systems of functional-differential equations in Sobolev space”, Sibirsk. Mat. Zh., 55:4 (2014), 851–862; Siberian Math. J., 55:4 (2014), 696–705
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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