Sample Period Effects in Optimally Designed Digital Control Systems

The effect of sample period on robustness and performance of a sampled data control system is considered. An optimal performance cost for a non-zero sample period may exist depending on the penalty weighting assigned to the system states. The robustness with respect to stability is investigated as a function of (a) the minimum singular value of an appropriate return difference matrix, in the discrete domain and (b) the mapping of the uncertainty, associated with unmodelled plant dynamics, from the continuous domain into the discrete domain.