Journal
SYSTEMS & CONTROL LETTERS
Volume 62, Issue 3, Pages 277-285Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2012.11.015
Keywords
Convergent systems; Incremental stability; Time-varying nonlinear systems; Converse Lyapunov result
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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. (C) 2012 Elsevier B.V. All rights reserved.
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