Traditional proportional-integral-based (PI-based) voltage balancing control (VBC) for single-phase cascaded H-bridge rectifiers (CHBR) suffer from unsatisfactory dynamic performance. An <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$-VBC approach is thus proposed in this paper to address this issue. The relationship between difference of dc-side voltage square and power is deduced

which is used to construct a new feedback closed-loop for VBC system. Compared with PI-based control method

the merit of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$ approach is tracking performance and disturbance suppression can be quantitatively solved through sensitivity weighting function. Considering external disturbance on control output

an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$-VBC strategy is designed for specified frequency bands. With the proposed method

dynamic performance of voltage balancing is improved. An experimental prototype is developed

and experiments are performed to verify effectiveness of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$-VBC strategy.