This paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple L₂-stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach.