This paper considers the design of decentralized digital control systems where the outputs are measured,vith different rates or at different times, whereas the inputs are updated all together, Specifically, a solution is given to the problem of asymptotically zeroing the system error when the exogenous signals coincide with the free motions of any unstable system, The proposed controller is constituted by a time-invariant internal model of the exogenous signals and a decentralized periodic stabilizer.