On strong regular stabilizability for linear 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, University of Szczecin
3 Department of Differential Equations and Control, Kharkov National University

The problem of strong stabilizability of linear systems of neutral type is investigated. We are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts. This is the case when the main part of the neutral equation is not assumed to be stable in the classical sense. We discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls. The method covers the case of multivariable control and is essentially based on the idea of infinite-dimensional pole assignment proposed in [G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls, C. R. Acad. Sci. Paris Ser. I Math. 333 (8) (2001) 807-812]. Our approach is based on the recent results on the Riesz basis of invariant finitedimensional subspaces and strong stability for neutral type systems presented in [R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations 214 (2) (2005) 391-428].

Mots clés: Neutral type systems; Regular stabilizability; Strong stabilizability; Infinite-dimensional systems

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

Rabah Rabah, Grigory M. Sklyar, Aleksandr V. Rezounenko. On strong regular stabilizability for linear neutral type systems. Journal of Differential Equations, 2008, 245 (3), pp.569-593. ⟨10.1016/j.jde.2008.02.041⟩. ⟨hal-00580044⟩