Fundamental finite controls with source-like disturbances of a general form

Fundamental finite control for disturbances representable through a nucleus and a fundamental set of finite controls are defined. Formulae are given which express fundamental finite control in terms of a fundamental set of finite controls. The problem of designing a fundamental set of finite controls is reduced to that of moments. For illustration, damping of small lateral oscillations is considered for a uniform string which rotates at a constant angular velocity. For such a system Fourier transform of the fundamental set of finite controls is found.