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On a Discrete-Time System Expressed in the Euler Operator

The Euler operator ¿ = (z-l)/T plays an important role in the analysis and synthesis of discrete-time systems. A number of properties pertaining to discrete-time systems which are expressed by the Euler operator approach those of continuous-time systems as the sampling frequency increases, and include those of discrete-time systems expressed by the z operator The stability criteria and some of the positive realness of a real rational function are among them However, there may be some properties which are different from the continuous-time counterpart even if the sampling frequency is increased. One such example is the relative degree condition of the positive real function.