Incremental global asymptotic stability equals incremental global exponential stability - but at equilibria.
Résumé
Incremental stability has become increasingly common in the context of nonlinear control. However, there is a lack of understanding of the difference between several notions of incremental stability. The objective of this paper is to show that the notion of incremental global asymptotic stability is very similar to that of incremental global exponential stability. In particular, nonexponential relaxation of the convergence rate appears only "locally" but not "globally." Some examples are provided to justify our theoretical arguments.
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