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Intelligent reflecting surface (IRS) is a promising 6G technology that can improve wireless communication capacity in a cost-effective and energy-efficient manner, by adjusting a large number of passive reflectors to appropriately change the signal propagation. In this study, we identified the achievable rate region of a two-hop interference channel with distributed multiple IRS relays. To do so, we formulated a non-convex problem that characterizes the rate-profile, and found its solution using successive convex approximation (SCA). We then proposed an alternating direction method of multipliers (ADMM) and alternating optimization (AO) based distributed and low-complex IRS control that maximizes the achievable sum-rate, and proved its convergence and optimality. We then compared the proposed IRS control with semi-definite relaxation (SDR)-, random phase-, deep reinforcement learning (DRL)- based IRS …