On the Singular Steady-State Output in Discrete-Time Linear Systems

摘要

The paper deals with discrete-time systems defined by difference equations whose transfer functions may have poles on the unit circle. Contrarily to the regular cases the eigenfunctions of these systems are no longer the exponentials. It is shown that if the input is a product of a falling factorial by an exponential the output is a linear combination of this kind of functions. In particular, the very useful and well-known ARIMA case is studied and exemplified.