Approximate z transform using higher-order integrators and its applications in sampled-data control systems

In this paper, we first clarify the difference between the approximate z transform and the discrete equivalent of a continuous system using higher-order integrators. It is shown that a 1/ t_s factor needs to be included for the approximate z transform but not for the discrete equivalent. We further apply the approximate z transform to facilitate the stability analysis of sampled-data control systems, with or without uncertain parameters, ft is shown in this paper that the approximate z transform greatly simplifies the stability analysis of a sampled-data control system, which is regarded as rather difficult (if not impossible) to handle because of its transcendental nature. The results can be easily obtained and show reasonably good approximations with this approach. Several examples are used to illustrate the effectiveness of this new method.