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About: Comparison function     Goto   Sponge   NotDistinct   Permalink

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In applied mathematics, comparison functions are several classes of continuous functions, which are used in stability theory to characterize the stability properties of control systems as Lyapunov stability, uniform asymptotic stability etc. Let be a space of continuous functions acting from to . The most important classes of comparison functions are: Functions of class are also called positive-definite functions. One of the most important properties of comparison functions is given by Sontag’s -Lemma, named after Eduardo Sontag. It says that for each and any there exist :