A control oriented approach to the time-discretization of delay systems

There are many examples of systems with delays, mainly due to transport phenomena, to the information transmission, to the calculation time of the integration digital devices, and so on. These systems, being infinite dimensional, are very difficult to analyze and to control. If they are forced by piecewise constant signals in time ranges of appropriate constant amplitude, such systems can be modeled by finite dimensional discrete-time systems. In this paper, theorems are stated that allow discretizing an LTI system with state, input and output delays, with an appropriate sampling period. A method is also proposed for the design of reduced order discrete-time controllers that allow assigning a set of arbitrary poles to the overall system. The accuracy of the discrete-time models and the effectiveness of the proposed controllers are illustrated by two interesting examples.