In this work, we address the computational challenges in personal audio systems implemented within a room environment, which typically operate under a multi-input multi-output (MIMO) framework. Traditional control algorithms require long control filters to prevent performance degradation, substantially increasing the computational load due to matrix inversion and overall system complexity. We introduce a novel approach utilizing second-order Kronecker product decomposition, where the loudspeaker control filter is expressed as the Kronecker product of two shorter sub-filters. This method effectively reduces the matrix dimensions required for a single filter, significantly lowering computational complexity compared to traditional time-domain techniques. An iterative filter design is then employed to closely approximate the globally optimal solution. Simulation results demonstrate that our method achieves performance comparable to that of the conventional algorithm while significantly reducing computational demands.