A decoupled sliding-mode neural network variable-bound control system (DSMNNVB) is proposed to control rotating stall and surge in jet engine compression systems in presence of disturbance and uncertainty. The control objective is to drive the system state to the original equilibrium point and it proves that the control system is asymptotically stable. In this controller, an adaptive neural network (NN) control scheme is employed for unknown dynamic of nonlinear plant without using a model of the plant. Moreover, no prior knowledge of the plant is assumed. The proposed DSMNNVB controller ensures Lyapunov stability of the nonlinear dynamic of the system.