Geodesic
On stabilization of a class of systems with time proportional delay
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 2, pp. 165-172

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In this paper, we investigate a possibility of the linear difference-differential system stabilization with time proportional delay by the linear observation. Using the sufficient conditions of asymptotic stability for the linear systems with linearly increasing delay, we obtain some conditions of the asymptotic evaluation system existence for the original system. Then we use the asymptotic evaluation system for the construction of the stabilizing control and derive the sufficient conditions for the existence of such control.
Keywords: system of linear differential-difference equations, linearly increasing time delay, asymptotic stability, stabilizing control, asymptotic evaluation system. 
@article{VSPUI_2018_14_2_a8,
     author = {A. P. Zhabko and O. G. Tikhomirov and O. N. Chizhova},
     title = {On stabilization of a class of systems with time proportional delay},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {165--172},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2018_14_2_a8/}
}
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A. P. Zhabko; O. G. Tikhomirov; O. N. Chizhova. On stabilization of a class of systems with time proportional delay. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 2, pp. 165-172. http://geodesic.mathdoc.fr/item/VSPUI_2018_14_2_a8/