This work focuses on observer's for one-dimensional (1D) Vlasov-Poisson (VP) system. Thanks to the discontinuous Galerkin method (DGM) to put the system into a suitable and explicit state space representation form. Then we construct a state observer of finite dimension that assures asymptotic convergence under weak conditions. Indeed, we introduce a useful Linear Parameter Varying System formulation to compute the observer gain matrix from a Linear Matrix Inequality. Moreover, since matrices obtained by the DGM are tridiagonal, we show that only a reduced order observer is necessary to estimate the whole state of the system. In the noise context, extension to H 8 state estimation is also established.