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Chapitre D'ouvrage Année : 2004

On strong stability and stabilizability of systems of neutral type

Résumé

For linear stationary systems, the infinite dimensional framework allows one to distinguish different notions of stability: weak, strong or exponential. The purpose of this chapler is to investigate the problem of strong stability, i.e. asymptotic non-exponential stability for linear systems of neutral type in order to use this characterization in the study of the stabilizability problem for this type of systems. An important tool in this investigation is the Riesz basis property of generalized eigenspaces of the neutral system, because that the generalized eigenvectors do not form, in general, a Riesz basis. This allows one to describe more precisely asymptotic non-exponential stability of neutral systems. For a particular case, conditions of strong stabilizability of neutral type systems are given with a feedback law without derivative of the delayed state.
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Dates et versions

hal-00819793 , version 1 (02-05-2013)

Identifiants

Citer

Rabah Rabah, Grigory M. Sklyar, Aleksandr V. Rezounenko. On strong stability and stabilizability of systems of neutral type. S. Niculescu, K. Gu. Advances in time-delay systems, Lect. Notes in Comp. Sci. Eng., vol 38, 2004, Springer, pp. 257-268, 2004, Lecture Note on Control and Information Sciences, ⟨10.1007/978-3-642-18482-6_19⟩. ⟨hal-00819793⟩
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