Abstract
The paper considers a mechanical system defined by a linear system of integro-differential equations with nonlocal convolution type terms. The problem of controllability is studied for various types of control (boundary and volume-distributed control) and various types of kernels. These kernels simulate the aftereffect of the system. It is proved that in some cases there is no possibility of damping the oscillations of the system for arbitrary initial conditions. In this work, those cases are distinguished when there is the possibility of damping oscillations over a finite period of time for any initial conditions.
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