Digital redesign of infinite-dimensional controllers based on numerical integration of new representation

Continuous-time infinite-dimensional controllers that include Laplace transforms of time functions with compact support are indispensable for the advanced control of delay systems. However, no study has yet been conducted on digital redesign for obtaining digital controllers that are used in sampled-data control systems from predesigned continuous-time infinite-dimensional controllers. We introduce a new representational form to describe the continuous-time input–output relation of linear time-invariant systems, called “finite interval integral representation”. Using numerical integration, we approximate the continuous-time input–output relation of a predesigned infinite-dimensional controller in the finite interval integral representation to obtain a digital controller.