Asymptotic attenuation and rejection for a class of cascade systems with general periodic disturbances

In this article, the problem of asymptotic attenuation and rejection is investigated for a class of cascade systems with general periodic disturbances via a non-linear disturbance observer and H ∞ control. First, a novel disturbance observer is developed to estimate general periodic disturbances, where the disturbances are described as a linear uncertain system with a non-linear output function. Then, a composite controller is constructed by combining the disturbance estimation with the partial state feedback control law, such that, the closed-loop system is asymptotically stable and meets H ∞ performance. With the help of the Lyapunov function theory and the linear matrix inequality method, some sufficient conditions for the desired controller and observer gains are established. Finally, numerical and application examples are presented to demonstrate the effectiveness of the proposed scheme.