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Journal Articles IEEE Control Systems Letters Year : 2022

New Versions of Halanay's Inequality with Multiple Gain Terms

Abstract

Halanay's inequality in its standard form is a widely used tool for the analysis of systems with delays and uncertainties, but the assumptions needed to use it are sometimes too restrictive to cover applications of interest. This paper provides new generalizations of Halanay's inequality where, instead of the usual supremum in the gain term in standard versions of Halanay's inequality, we use a weighted sum of suprema over different intervals. This allows us to derive sufficient conditions for asymptotic and input-to-state stability. We apply our results to linear systems with switched delays and other examples that illustrate how our results are less restrictive than those of other contributions available in the literature.
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Dates and versions

hal-03711601 , version 1 (01-07-2022)

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Frederic Mazenc, Michael Malisoff. New Versions of Halanay's Inequality with Multiple Gain Terms. IEEE Control Systems Letters, 2022, ⟨10.1109/LCSYS.2021.3133214⟩. ⟨hal-03711601⟩
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