Generalized reciprocally convex combination lemmas and its application to time-delay systems. (English) Zbl 1402.93193
Summary: 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 Y. S. Moon et al.’s inequality [Int. J. Control 74, No. 14, 1447–1455 (2001; Zbl 1023.93055)], 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 [H. Shao, Automatica 45, No. 3, 744–749 (2009; Zbl 1168.93387)] 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.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 15A45 | Miscellaneous inequalities involving matrices |
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