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• W3089346066 endingPage "6715" @default.
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• W3089346066 abstract "Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semicontractive) systems, the distance (resp. semidistance) between any two trajectories decreases exponentially fast. For partially contractive systems, each trajectory converges exponentially fast to an invariant subspace. In this article, we develop contraction theory on Hilbert spaces. First, we provide a novel integral condition for contractivity, and for time-invariant systems, we establish the existence of a unique globally exponentially stable equilibrium. Second, we introduce the notions of partial and semicontraction and we provide various sufficient conditions for time-varying and time-invariant systems. Finally, we apply the theory on a classic reaction-diffusion system." @default.
• W3089346066 created "2020-10-08" @default.
• W3089346066 creator A5014088551 @default.
• W3089346066 creator A5048861319 @default.
• W3089346066 creator A5068353454 @default.
• W3089346066 date "2022-12-01" @default.
• W3089346066 modified "2023-09-23" @default.
• W3089346066 title "Contraction Theory for Dynamical Systems on Hilbert Spaces" @default.
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• W3089346066 doi "https://doi.org/10.1109/tac.2021.3133270" @default.
• W3089346066 hasPublicationYear "2022" @default.
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