About stabilization by feedback control in integral form

In this paper we demonstrate that in many cases the investigation of the problem of controlling chaos, which is of great theoretical and practical importance, can be reduced to the stability analysis of the corresponding integro-differential equations. We consider stabilization for the configuration of a magneto-elastic beam and a two magnet system known as “Moon's beam”. Then we study an unstable system, in which the Lorenz attractor appears, and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of integrodifferential equations to systems of ordinary differential equations.