On cone perturbing Liapunov function for impulsive differential systems

The concept of ϕ0-stability and ϕ0-boundedness recently were introduced for systems of ordinary differential equations (ODEs). Perturbing Liapunov function method was discussed for systems of ODEs and extend to systems of functional differential equations (FDEs). In this paper, we extend these notions to impulsive systems of differential equations via cone perturbing Liapunov function method.