On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Differential Equations Year : 2012

On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping

Abstract

We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinite-dimensional then the system needs not being asymptotically stable (not even in the weak sense). Exponential stability is recovered under a generalized observability inequality, allowing for time-domains that are not intervals. Weak asymptotic stability is obtained under a similarly generalized unique continuation principle. Finally, strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition, evaluating their total contribution to the decay of the trajectories of the damped system. Our results are discussed using the example of the wave equation, Schrödinger's equation and, for strong stability, also the special case of finite-dimensional systems.
Fichier principal
Vignette du fichier
PE-hilbert-post.pdf (251.58 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00616474 , version 1 (22-08-2011)
inria-00616474 , version 2 (10-02-2012)

Identifiers

Cite

Falk Hante, Mario Sigalotti, Marius Tucsnak. On conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping. Journal of Differential Equations, 2012, 252 (10), pp.5569-5593. ⟨10.1016/j.jde.2012.01.037⟩. ⟨inria-00616474v2⟩
454 View
374 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More