On the role of sampling zeros in robust sampled-data control design

In this paper, we investigate the implications for robust sampled-data feedback design of minimum phase sampling zeros appearing in the transfer function of discrete-time plants. Such zeros may be obtained by zero-order hold (ZOH) sampling of continuous-time models having relative degree two or greater. In particular, we address the robustness of sampled-data control systems to multiplicative uncertainty in the model of the continuous-time plant. We argue that lightly damped controller poles, which may arise from attempting to cancel, or almost cancel, sampling zeros of the discretized plant are likely to introduce peaks into the fundamental complementary sensitivity function near the Nyquist frequency. This in turn makes the satisfaction of necessary conditions for robust stability difficult for all but the most modest amounts of modeling uncertainty in the continuous-time plant. Some H2082₂- and H∞-optimal discrete-time and sampled data designs may lead to (near-) cancellation, and we therefore argue that their suitability is restricted