Stability of linear functional differential systems with multivalued delay feedback

Abstract

We consider a controlled linear functional differential system with linear feedback without delay and assume that the closed system is exponentially stable. Then we assume a non-ideality in the feedback loop such that it has an unknown delay, which may be distributed or not. We suppose that this delay is sufficiently small. In such a case, the disturbed system is presented by a functional differential inclusion of special type. We prove that this inclusion remains exponentially stable. To do this, we use the exponential estimate, which is valid uniformly for all Cauchy functions of some class of linear functional differential equations that are close to given one.