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Cell-free networks are considered to be a promising distributed network architecture to satisfy the increasing number of users and high rate expectations in beyond-5G systems. However, to further enhance network capacity, an increasing number of high-cost base stations (BSs) is required. To address this problem and inspired by the cost-effective intelligent reflecting surface (IRS) technique, we propose a fully decentralized design framework for cooperative beamforming in IRS-aided cell-free networks. We first transform the centralized weighted sum-rate maximization problem into a tractable consensus optimization problem, and then an incremental alternating direction method of multipliers (ADMM) algorithm is proposed to locally update the beamformer. The complexity and convergence of the proposed method are analyzed, and these results show that the performance of the new scheme can asymptotically …