A note on aperiodicity condition for linear discrete systems

In this note conditions for the roots of a real polynomial to lie in the segment [0, 1), i.e., aperiodicity condition is obtained. The conditions obtained are based on a nonlinear transformation which transforms the segment [0, 1) onto the periphery of the unit circle. The results of this note correct the earlier proposed corollary obtained by Szaraniec using this transformation and present a test for verifying the aperiodicity condition.