Linearized stability for a class of neutral functional differential equations with state-dependent delays

In this paper we formulate a stability theorem by means of linearization around a trivial solution in the case of autonomous neutral functional differential equations with state-dependent delays. We prove that if the trivial solution of the linearized equation is exponentially stable, then the trivial solution of the nonlinear equation is exponentially stable as well. As an application of the main result, explicit stability conditions are given.