Abstract: For a contactless battery charging system based on inductively coupled power transfer technology, a generalized state-space averaging method is first introduced, which can convert the original system with the oscillating and nonlinear characteristics to a linear time-invariant system by using the low-order Fourier series to approximate the original circuit signals and nonlinear terms and then the performance weighting functions for multi-objective optimization are adjusted and chosen in the frequency domain to reflect the uncertainties of low frequency parameters and high frequency un-modeled part. To fulfill a robust stability and robust performance design in the constant-current mode, a H∝ synthesis control algorithm solved by the linear matrix inequality method is proposed for the contactless battery charging system. All the results of computer simulation and practical experiment show that with the help of H∝ control strategy, the system has successfully realized operating at the constant-current charging mode, dynamically tracking the current reference according to the battery charging requirements, rapidly inhibiting the adverse effects of battery voltage changes and load or frequency perturbations on the system. Therefore, the H∝ control strategy used for contactless battery charging system is effective and practicable.