On the output control of multirate systems subject to arbitrary exogenous signals

The design of multi-input, multi-output (MIMO) digital control systems in which each plant output is sampled at its own rate, whereas the inputs are updated all together, is considered. Specifically, a solution is given to the problem of asymptotically zeroing the system error when the exogenous signals coincide with the free motion of any unstable system. The proposed controller consists of a time-invariant internal model of the exogeneous signals and a periodic stabilizer