  Intelligent reflecting surfaces (IRSs) have emerged as a promising economical
solution to implement cell-free networks. However, the performance gains
achieved by IRSs critically depend on smartly tuned passive beamforming based
on the assumption that the accurate channel state information (CSI) knowledge
is available, which is practically impossible. Thus, in this paper, we
investigate the impact of the CSI uncertainty on IRS-assisted cell-free
networks. We adopt a stochastic programming method to cope with the CSI
uncertainty by maximizing the expectation of the sum-rate, which guarantees
robust performance over the average. Accordingly, an average sum-rate
maximization problem is formulated, which is non-convex and arduous to obtain
its optimal solution due to the coupled variables and the expectation operation
with respect to CSI uncertainties. As a compromising approach, we develop an
efficient robust joint design algorithm with low-complexity. Particularly, the
original problem is equivalently transformed into a tractable form, and then,
the locally optimal solution can be obtained by employing the block coordinate
descent method. We further prove that the CSI uncertainty impacts the design of
the active transmitting beamforming of APs, but surprisingly does not directly
impact the design of the passive reflecting beamforming of IRSs. It is worth
noting that the investigated scenario is flexible and general, and thus the
proposed algorithm can act as a general framework to solve various sum-rate
maximization problems. Simulation results demonstrate that IRSs can achieve
considerable data rate improvement for conventional cell-free networks, and
confirm the resilience of the proposed algorithm against the CSI uncertainty.
