On Exact Controllability and Complete Stabilizability for Linear Systems in Hilbert Spaces

Rabah Rabah (1) , Jamila Karrakchou

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

A criterion of exact controllabilty using the resolvent of the state space operator is given for linear control system in Hilbert space . Only surjectivity of the semi-group operators is assumed. This condition is necessary for exact controllability, so the criterion is quite general. Relations between exact controllability and complete stabilizability are specified.

Mots clés: Infinite dimensional systems; linear systems; exact controllability; stabilizability

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

Rabah Rabah, Jamila Karrakchou. On Exact Controllability and Complete Stabilizability for Linear Systems in Hilbert Spaces. Applied Mathematics Letters, 1997, 10 (1), pp. 35--40. ⟨10.1016/S0893-9659(96)00107-3⟩. ⟨hal-00819342⟩