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, is studied. In particular, it is shown that when state-space descriptions of linear SISO continuous-time systems with relative degree ⩾2 are discretized, then the zero dynamics of the resulting discrete system is singularly perturbed and shows a separation of time scale. The part of the zero dynamics associated with the fast time scale is shown to correspond to the zeros introduced by the sampling process (sampling zeros). An asymptotic formula for this part of the zero dynamics is given, and implications of the result to control design based on pole zero cancellation is discussed