This paper proposes an uncertain rule-based fuzzy neural system (UFNS-S) with stable learning mechanism for nonlinear systems identification and control. The proposed UFNS-S system not only preserves the ability of handling uncertain information but also performs less computational effort. The sinusoidal perturbations are adopted to combine with the fuzzy term sets of UFNS-S. For training the UFNS-S systems on system identification and control applications, the gradient descent method with adaptive learning rate is derived. This guarantees the convergence of UFNS-S by choosing adaptive learning rates which enhance the convergent speed. This provides a simple way for choosing the learning rates for training the UFNS-S which also guarantees convergence and faster learning. Finally, the effectiveness and performance of the proposed approach is illustrated by several examples, computational complexity analysis, nonlinear system identification, and tracking control of two-link robot manipulator system.