In this paper, we address the problem of exponential stability for a class of linear hyperbolic systems with distributed sampled-data control. First, we recast the original system into a hybrid model via an augmented system approach. Using this model, the link between the sampling interval, the system state and its sampled vector is characterized by an Integral Quadratic Constraint (IQC). The obtained IQC is used for deriving numerically tractable stability criteria. The method is illustrated by an open loop unstable numerical example.