Lipschitz stability of differential equations with supremum and non-instantaneous impulses

Lipschitz stability for nonlinear differential equations with non-instantaneous impulses and supremum of the unknown function over a past time interval is studied. The impulses start abruptly at some points and their action continue on given finite intervals. Some sufficient conditions for Lipschitz stability are obtained. Modified Razumikhin method with piecewise continuous functions and comparison results with scalar non-instantaneous equations are applied.