Bode´s integral theorem for discrete-time systems

A paper by Bode (1945) has shown the limitations of using a feedback structure in terms of an integral constraint on the sensitivity function for open-loop stable continuous-time systems. The present paper examines and derives equivalent results for discrete-time feedback systems. These integral constraints also provide some guidelines regarding the philosophy of feedback design specifically for sampled-data systems. For example, it is shown that, for all sampled-data control systems, there is a maximum sampling frequency, beyond which little improvement in performance is gained.