On global stability of nonlinear systems with unbounded and distributed delays and a dominating non-delay term

A system with, generally, unbounded and non-continuous delays is considered as a perturbation of a linear non-delay system. Boundedness of solutions, stability, global asymptotic stability, uniform exponential stability are established with a variety of methods, including designing a Lyapunov-Krasovskii functional and integral transformations. The system incorporates a linear non-delay part and a sum of either linear or nonlinear terms, dependent on several time-variable delays. The dependency of the stability type on the delay properties is outlined and illustrated with examples. • A general nonlinear system with variable coefficients and delays is considered. • Boundedness, solution estimates and stability are explored by a variety of methods. • Examples illustrate convergence and sharpness of the assumptions of the theorems. • Both delay-dependent and delay-independent stability results are obtained.