Weighted exponential stability for generalized delay functional differential equations with bounded delays

Abstract

In the paper functional differential equations with several bounded delays are considered. The delays are presented in the form of delay operators and they generalize many well-known types of delay differential equations in the literature, such as differential equations with constant delays, with variable delays, with distributed delays, differential equations with maxima, etc. A special type of stability, known as ψ-exponential stability, is studied and several sufficient conditions are obtained. The used function ψ plays the role of a weight in the norm and, additionally, it gives the rate of increase of the solutions which are not exponentially stable in the regular sense. The modified Razumikhin method as well as comparison results have been applied. Several examples illustrate the results obtained. MSC:34K20.