Uniform global asymptotic stability of differential inclusions

Stability of differential inclusions defined by locally Lipschitz compact valued mappings is considered. It is shown that if such a differential inclusion is globally asymptotically stable, then, in fact, it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact- (not necessarily convex-) valued differential inclusions. The main result is presented in a context which is useful for control-theoretic applications: a differential inclusion with two outputs is considered, and the result applies to the property of global error detectability.