A quasi-ARX (quasi-linear ARX) neural network (QARXNN) model is able to demonstrate its ability for identification and prediction highly nonlinear system. The model is simplified by a linear correlation between the input vector and its nonlinear coefficients. The coefficients are used to parameterize the input vector performed by an embedded system called as state dependent parameter estimation (SDPE), which is executed by multi layer parceptron neural network (MLPNN). SDPE consists of the linear and nonlinear parts. The controller law is derived via SDPE of the linear and nonlinear parts through switching mechanism. The dynamic tracking controller error is derived then the stability analysis of the closed-loop controller is performed based Lyapunov theorem. Linear based adaptive robust control and nonlinear based adaptive robust control is performed with the switching of the linear and nonlinear parts parameters based Lyapunov theorem to guarantee bounded and convergence error.