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The control of a linear time-invariant plant by a digital controller composed of a sampler, a periodic discrete-time component, and a zero-order hold is considered. The stability of such a configuration is analyzed. It is shown how closed-loop zeros can be placed using such a scheme. As a consequence, it is proved that the gain margin can be arbitrarily assigned by suitable choice of sampling time and digital controller. The design procedure is constructive, using state-space methods.>
Francis et al. (Thu,) studied this question.