ABSTRACT
Noise in the control systems is one of the reasons to consider distributed feedback control. In the study of stability of integro-differential equations, which can describe formally the models with distributed feedback control, the following assumption was done. The “ordinary part” of integro-differential system is supposed to be exponentially stable and the “integral part” - to be “small enough”. In application usually we have the opposite situation where the “ordinary part” is unstable and the exponential stability has to be achieved by adding the distribute feedback control, i.e. by the “integral part”. Although stabilizing systems by distributed feedback control is now a challenging problem, only a few publications were devoted to it.
In this chapter, results on stabilization by delay distributed feedback control are obtained. It is demonstrated that infinite memory does not disturb the exponential stability and in many cases could even help to achieve it. A simple method to reduce integro-dfferential systems of the order n to systems of ordinary differential equations of the order n+m is proposed.
