The purpose of this paper is to study the determination of L ₂ gain performance index in a design method of anti-windup compensator. Since the purpose of the anti-windup compensation is to control the controller state, we introduce a new L ₂ gain performance index that contains both the plant state and the controller state. Local control design technique which is based on the circle criterion is used for anti-windup compensator synthesis, while global control performance analysis is conducted using Popov criterion. Better response is obtained by tuning the two weighting matrices on the states of the performance index, which is demonstrated by simulation and experiment examples.