 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.S. Andreev and O.A. Peregudova, "Lyapunov Functional Method in the Stability Problem of Volterra Integro-Differential Equations with Infinite Delay," Mech. Solids. 56 (8), 1514-1533 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1514-1533 |
| DOI |
10.3103/S0025654421080033 |
| Title |
Lyapunov Functional Method in the Stability Problem of Volterra Integro-Differential Equations with Infinite Delay |
| Author(s) |
A.S. Andreev (Ulyanovsk State Technical University, Ulyanovsk, Russia, asa5208@mail.ru)
O.A. Peregudova (Ulyanovsk State Technical University, Ulyanovsk, Russia, peregudovaoa@gmail.com) |
| Abstract |
The paper considers the stability problem for a non-autonomous nonlinear integro-differential equation of Volterra type with infinite delay. The development of the Lyapunov functional
method is carried out in both the limiting behavior study of a bounded solution as well as the asymptotic stability of the zero solution in all and some of the variables under the assumption of the corresponding Lyapunov functional existence with a semi-definite time derivative. The problems on the
study of the motion limiting properties for a mechanical system with linear heredity as well as the stationary motion stabilization of a manipulator with viscoelastic cylindrical and spherical joints are
solved. The control problem of a five-link robot manipulator is solved taking into account the visco-elasticity of its joints. |
| Keywords |
Volterra integro-differential equations, stability, Lyapunov functional, mechanical system with viscoelastic elements, manipulator, control |
| Received |
27 February 2021 | Revised |
08 March 2021 | Accepted |
19 March 2021 |
| Link to Fulltext |
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