On uniform stability of nonlinear measure differential equations

This paper investigates uniform stability and uniformly asymptotical stability of nonlinear measure differential equations in Banach spaces. This general system can model a large class of hybrid systems without any restriction on their Zeno behavior. The sufficient conditions of uniform stability and uniformly asymptotical stability for the system are obtained by using Lyapunov functions, in the lack of Lipschitz continuity assumptions. Then less conservative stability criteria for impulsive differential equations than those in the literature are deduced as a special case.