Adaptive stability control can be made more applicable by incorporating it into the estimator of nonlinear time variant uncertainties. In order to achieve input-to-state stability (ISS) with respect to unknown bounded disturbances, the backstepping and control Lyapunov function (CLF) techniques were used to design an adaptive controller of full-state feedback for certain cascade nonlinear systems. It shows that update laws can estimate unknown bounded disturbances. This requires less information on the disturbance as a part of the stabilizing control law. This design method achieves the desired property: robust global asymptotical stability. The results of the illustrative example in the disturbed pendulum show that some advances are made in stabilizing cascade nonlinear system with the unknown disturbance.