Razumikhin method and cone valued Lyapunov functions for impulsive differential equations with 'supremum'

Abstract

Stability of nonlinear impulsive differential equations with 'supremum' is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.