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A new method using adaptive sliding mode back-stepping control is presented for indirect four-leg matrix converter. It is robust against uncertain loads and control input disturbance due to the interaction between input filter and matrix converter. The input currents are analyzed under unbalanced and nonlinear loads, which helps to design a proper input filter to attenuate the harmonics flowing into power grid. A varying period carrier-based modulation is introduced to indirect four-leg matrix converter which makes it easier to implement. Both simulations and experimental results verify the feasibility of the proposed method.