Stability and error analysis of the anti-causal realization of periodic inverse systems

A causal realization of an inverse system can be unstable and an anti-casual realization is to deal with this problem to provide a numerically stable procedure to inverse the system and compute its input signal. In this paper, we consider the anti-causal realization of the inverse of discrete time linear periodic systems obtained by an outer-inner factorization approach. It is shown that the outer-inner factorization can result in a stable anti-causal realization. An expression of the inversion error is derived, showing such an error is inevitable due to the anti-causal reversal operation.