Geodesic
Stability analysis of mechanical systems with distributed delay via decomposition
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 13-26

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The article analyzes a linear mechanical system with a large parameter at the vector of velocity forces and a distributed delay in positional forces. With the aid of the decomposition method, conditions are obtained under which the problem of stability analysis of the original system of the second-order differential equations can be reduced to studying the stability of two auxiliary first-order subsystems. It should be noted that one of the auxiliary subsystems does not contain a delay, whereas for the second subsystem containing a distributed delay, the stability conditions are formulated in terms of the feasibility of systems of linear matrix inequalities. To substantiate this decomposition, the Lyapunov direct method is used. Special constructions of Lyapunov—Krasovskii functionals are proposed. The developed approach is applied to the problem of monoaxial stabilization of a rigid body. The results of a numerical simulation are presented confirming the conclusions obtained analytically.
Keywords: mechanical system, stability, distributed delay, rigid body, Lyapunov—Krasovskii functionals.
Mots-clés : decomposition 
@article{VSPUI_2021_17_1_a1,
     author = {A. Yu. Aleksandrov and A. A. Tikhonov},
     title = {Stability analysis of mechanical systems with distributed delay via decomposition},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {13--26},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a1/}
}
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A. Yu. Aleksandrov; A. A. Tikhonov. Stability analysis of mechanical systems with distributed delay via decomposition. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 13-26. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a1/