Relative Error Issues in Sampled Data Models

Most real world systems operate in continuous time. However, to store, analyze or transmit data from such systems the signals must first be sampled. Consequently there has been on-going interest in sampled data models for continuous time systems. The emphasis in the literature to-date has been on three main issues namely the impact of folding, sampled zero dynamics and the associated model error quantification. Existing error analyses have almost exclusively focused on unnormalized performance. However, in many applications relative errors are more important. For example, high performance controllers tend to invert the system dynamics and consequently relative errors underpin closed loop performance issues including robustness and stability. This motivates us to examine the relative errors associated with several common sampled data model types. This analysis reveals that the inclusion of appropriate zero dynamics is essential to ensure that the relative error converges to zero as the sampling period is reduced.