On exponential stability of generalized linear functional differential equations

Abstract

We develop a general approach to uniform exponential stability for a broad class of linear functional differential equations with Volterra operators. The considered class includes delay differential equations, integro-differential equations, equations with distributed delays, vector equations, and systems of scalar functional differential equations. Standard assumptions on the equation are relaxed to include measurable parameters. Some results remain valid for equations with unbounded delays and oscillatory coefficients and kernels. For all the above mentioned classes of equations, explicit uniform exponential stability tests are obtained.

31 pages