Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 36, pp. 1-14.
Title: Stability of linear functional differential systems with
multivalued delay feedback
Author: Vadim Z. Tsalyuk (Kuban State Univ., Krasnodar, Russia)
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.
Submitted January 18, 2007. Published February 27, 2007.
Math Subject Classifications: 34K20, 34K35.
Key Words: Linear functional differential equations; Cauchy function;
functional differential inclusions; exponential stability.