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Lyapunov Functional Method in the Stability Problem of Volterra Integro-Differential Equations with Infinite Delay

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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 viscoelasticity of its joints.

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  1. Ulyanovsk State Technical University, Ulyanovsk, Russia

    A. S. Andreev & O. A. Peregudova

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  1. A. S. Andreev
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  2. O. A. Peregudova
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Andreev, A.S., Peregudova, O.A. Lyapunov Functional Method in the Stability Problem of Volterra Integro-Differential Equations with Infinite Delay. Mech. Solids 56, 1514–1533 (2021). https://doi.org/10.3103/S0025654421080033

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