Discrete-time positive-real lemma revisited: the discrete-time counterpart of the Kalman-Yakubovitch lemma

In this paper, we present what can be considered the discrete-time counterpart of the concept of positive realness and the corresponding algebraic necessary and sufficient criteria that a discrete-time transfer function matrix must satisfy. This latter result may be thought of as the discrete-time counterpart of the Kalnan-Yakubovitch lemma and it is expected to find application in various areas of study. In particular, its use in proving the Jury-Lee criterion applicable in absolute stability studies of a certain class of discrete-time nonlinear systems is shown.>