Sampling schemes in sampled-data control systems

In the early development of the sampled-data field, it was assumed that the sampling pattern is periodic with fixed period T, that the pulse width is of negligible duration, and that these short pulses are represented by impulses. Based on this representation, several analysis methods were developed, among them the s-transform method [1]–[3], the difference equation [4]–[6], and the state-variable approach [6], [7]. Following recent extension and research in this field, these preliminary assumptions have been relaxed to a large extent, so that wider application and more general methods of analysis could be developed. In the discussion of the first category on the fixed sampling pattern, it can be easily observed that the s-transform method with its various extensions is applicable to deal with all the indicated cases.