Journal
AUTOMATICA
Volume 95, Issue -, Pages 488-493Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2018.06.017
Keywords
Time-delay systems; Matrix inequalities; Generalized reciprocally convex lemmas
Funding
- ANR project SCIDiS contract [15-CE23-0014]
- National Natural Science Foundation of China [61503026, 61720106010]
- Beijing Natural Science Foundation [4182057]
- Foundation of Beijing Institute of Technology [3060011181811]
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Various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time-varying delays. This paper provides more insights on the relationship between some of them. We present an equivalent formulation of Moon et al.'s inequality, allowing us to discover strong links not only with the most recent and efficient matrix inequalities such as the reciprocally convex combination lemma and also its relaxed version but also with some previous inequalities such as the approximation inequality introduced in Shao (2009) or free-matrix-based inequality. More especially, it is proved that these existing inequalities can be captured as particular cases of Moon et al.'s inequality. Examples show the best tradeoff between the reduction of conservatism and the numerical complexity. (C) 2018 Elsevier Ltd. All rights reserved.
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