Integral characterizations of uniform asymptotic and exponential stability with applications

We present integral characterizations of uniform asymptotic stability and uniform exponential stability for differential equations and inclusions. These characterizations are used to establish new results on concluding uniform global asymptotic stability when uniform global stability is already known and uniform convergence must be established by additional arguments. In one case we generalize Matrosov's theorem on the use of a differentiable auxiliary function. In another case we draw conclusions from a system related to the original by suitable output injection.