Zeros of discretized continuous systems expressed in the Euler operator-an asymptotic analysis

The structure of the zeros of SISO continuous time systems which are discretized via a zero order hold and expressed in the Euler operator, ε (ε=(x-1)/T), is studied. It is shown that when state space descriptions of linear SISO continuous time systems with relative degree ≥2 are discretized, the zero dynamics of the resulting discrete system is singularly perturbed and shows a reparation of time scale; the fast time scale corresponding to the zeros introduced by the sampling process. Finally, implications of the result to control design based on pole zero cancellation is discussed.