Convergent systems vs. incremental stability

B.S. Rüffer; N. Wouw, van de; M. Mueller

doi:10.1016/j.sysconle.2012.11.015

Convergent systems vs. incremental stability

B.S. Rüffer, N. Wouw, van de, M. Mueller

Dynamics and Control

Research output: Contribution to journal › Article › Academic › peer-review

82 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	277-285
Number of pages	9
Journal	Systems and Control Letters
Volume	62
Issue number	3
DOIs	https://doi.org/10.1016/j.sysconle.2012.11.015
Publication status	Published - 2013

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title = "Convergent systems vs. incremental stability",

abstract = "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.",

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AU - Wouw, van de, N.

AU - Mueller, M.

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AB - 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.

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DO - 10.1016/j.sysconle.2012.11.015

M3 - Article

SN - 0167-6911

VL - 62

SP - 277

EP - 285

JO - Systems and Control Letters

JF - Systems and Control Letters

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Convergent systems vs. incremental stability

Abstract

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