Convergent systems vs. incremental stability. (English) Zbl 1261.93072

Summary: Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions.


93D30 Lyapunov and storage functions
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
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