Abstract
This chapter investigates the dynamics of a system modeled by a retarded functional differential equation (RFDE) when the system is subjected to high-frequency perturbations introduced in a special way: through the feedback mechanism. A classical example is the stabilization of a pendulum at the vertical position by rapidly oscillating the support. In fact, this class of perturbations is used successfully in control theory to stabilize systems of ordinary differential equations (ODE). The classical method of averaging for ODEs is the appropriate tool for understanding the effects of high-frequency perturbations. The chapter aims to reformulate the classical result for ODEs and the extension to RFDEs under the additional assumption that the delay r in the system is O(∊).
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