Almost Disturbance Decoupling for a Class of Fractional-Order Nonlinear Systems with Zero Dynamics

The problem of almost disturbance decoupling is addressed for fractional-order nonlinear systems. A new definition for the norm is proposed to describe the effect of disturbances on the output tracking error for fractional-order systems. Based on the Lyapunov stability theory and the backstepping design method, a tracking controller is constructed to make the output tracking error converge to zero without external disturbances and to attenuate the effect of disturbances on the tracking error at zero initial conditions. In order to validate these theoretical results, a numerical example and two practical examples are given.