Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a multilayer recurrent neural network is presented for robust pole assignment in synthesizing output feedback control systems. The proposed recurrent neural network is composed of three layers and is shown to be capable of synthesizing linear output feedback control systems via robust pole assignment in real time. Convergence of the neural network can be guaranteed. Moreover, with appropriate design parameters the neural network converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the neural network is globally exponentially stable. These desired properties make it possible to apply the proposed recurrent neural network to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed neural network approach.