Geodesic
Liapunov--Krasovskii quadratic functionals for linear autonomous systems with aftereffect
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 48-56

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In this paper the converse problem of asymptotic stability theorem for linear autonomous systems with aftereffect are examined. Analytic representations Liapunov–Krasovskii quadratic bounded positive functionals in Hilbert space are investigated.
Keywords: differential equations with aftereffect, stability, quadratic functionals. 
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     author = {Yu. F. Dolgii},
     title = {Liapunov--Krasovskii quadratic functionals for linear autonomous systems with aftereffect},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     number = {5},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a6/}
}
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Yu. F. Dolgii. Liapunov--Krasovskii quadratic functionals for linear autonomous systems with aftereffect. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 5, pp. 48-56. http://geodesic.mathdoc.fr/item/TIMM_2010_16_5_a6/