Abstract
We present an integral characterization of uniform asymptotic stability for differential equations and inclusions. This characterization is 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. We show the utility of our result by generalizing Matrosov's Theorem on the use of a differentiable auxiliary function. Also, we present an application to the stability analysis of time-varying systems.
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