This brief implements the singular pencil model and the extended Kalman filter to estimate the states and parameters simultaneously with unknown noise. Combined with state feedback predictive control, the proposed method can incorporate online estimation of both states and parameters and the controller design. Stability and observability of the states and parameters vector are analyzed. Simulation and online implementation in proton exchange membrane (PEM) fuel cell flow systems illustrate the strong disturbance rejection ability of this method. This brief uses the adaptive state feedback predictive controller, which based on the singular pencil model method, to control the cathode pressure and the proportional-integral (PI) controller to control the anode pressure. The proposed method works well to track the dynamics of the process at an idle and a given load.