Asymptotic attenuation and rejection for systems with general periodic disturbances via nonlinear disturbance observer and H∞ control

In this paper, the problem of asymptotic attenuation and rejection for systems with general periodic disturbances via nonlinear disturbance observer and H∞ control is investigated. A composite controller is constructed by combining the disturbance estimation value with state feedback control law, which can guarantee the closed-loop system asymptotical stability with H∞ performance. Some sufficient conditions for the desired controller and observer gains are established by linear matrix inequalities and Lyapunov function methods. Finally, a numerical example is used to demonstrate the effectiveness of the proposed scheme.