Motion of a system of oscillators under the generalized dry friction control

Abstract

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to equilibrium. The problem of existence and uniqueness of motion under the suggested control is resolved within the framework of the DiPerna--Lions theory of singular ordinary differential equations.