A general linear controller design method for a class of hyperbolic linear partial differential equation (PDEs) systems is presented. This is achieved by using an infinite-dimensional Hilbert state-space description with infinite-dimensional (distributed) input and output. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem, where one elementary reaction takes place. An optimal controller is designed for linearized fixed-bed reactor model, it is applied to the original nonlinear model and the resulting closed-loop stability is analyzed. Numerical simulations are performed to show the performance of the designed controller. (C) 2009 Elsevier Ltd. All rights reserved.