Generalized Riesz basis property in the analysis of neutral type systems

Rabah Rabah (1) , Grigory M. Sklyar (2) , Aleksandr V. Rezounenko (3)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 Institute of Mathematics
3 Department of Differential Equations and Control

The functional differential equation of neutral type is studied. We consider the corresponding operator model in Hilbert space M2 = Cn × L2(−1, 0;Cn) and prove that there exists a sequence of invariant finite-dimensional subspaces which constitute a Riesz basis in M2. We also give an example emphasizing that the generalized eigenspaces do not form a Riesz basis.

Mots clés: Neutral type systems; Riesz basis; spectral systems

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Rabah Rabah, Grigory M. Sklyar, Aleksandr V. Rezounenko. Generalized Riesz basis property in the analysis of neutral type systems. Comptes Rendus. Mathématique, 2003, I 337 (1), pp.19--24. ⟨10.1016/S1631073X(03)00251-6⟩. ⟨hal-00819154⟩