Compared with the conventional active power filter (APF), the static var compensator coupling hybrid active power filter(SVC-HAPF) has distinct characteristics of low DC-link operating voltage, which can lower the system and operational costs. It also has a wider operational range than the conventional hybrid active power filter(HAPF). In this paper, a harmonic state-space(HSS) modeling is firstly proposed to address the nonlinearity issue of the SVC-HAPF. The HSS based SVC-HAPF model is linear time-invariant(LTI), which enables the optimal control techniques. Then, the linear matrix inequality(LMI) based H∞ optimal control design is proposed, which finds the optimal controller parameters via convex optimization algorithm. The proposed controller for the SVC-HAPF achieves high steady-state accuracy, fast transient response, and fixed switching frequency simultaneously. Finally, simulation and experimental results are also provided to verify the effectiveness and performance of the optimal controller for the SVC-HAPF in comparison with the recent developed state-of-the-art multi-quasi-proportional-resonant (MQPR) controller, which shows superior control performances.