Time-varying uncertainties and load variation will influence the stabilization of active power filter control system.In order to enhance disturbance suppression capability and robustness

a state-space model which includes outside interference was established for APF based on H∞ control theory.An H∞ output-feedback robust controller was designed for the single phase shunt APF using linear matrix inequality.The controller can compensate the aberration rate of power grid from 28.93% to less than 3% in 2～3 cycle

and when the load current changes

the rapid dynamic compensation and high-precision steady-state compensation still can be achieved.The controller not only ensures the stability of the close-loop system and the stronger interference suppression ability

but also owns an effective dynamic compensation.