On state feedback control of a class of NonLinear PDE systems in finite dimension

Abstract

In this note, we propose some new results on state feedback stabilization of a class of non linear PDE systems that are described by Vlasov-Poisson equations. For doing so, thanks to the Galerkin discontinuous discretization approach, we establish first an explicit state space model in finite dimension. A state feedback controller is then proposed. One of the main futures is that the asymptotic stabilization may be guaranteed under an easy tractable LMI condition. Extension to the observer based control case, in the presence of disturbances or not, was also established. We provide an LMI condition to assure convergence in the H∞ sense.