On the stability of invariant sets of functional differential equations Original Research Article

A system of functional differential equations with delay dz/dt=Z(t,zt), where z=(x,y),x∈Rn, y∈Rm, and Z is the vector-valued functional, is considered. It is supposed that this system has a positive invariant set x=0. Definitions of its stability, asymptotic stability, and uniform asymptotic stability are given. Theorems on the uniform asymptotic stability are formulated and proved.