On Fixed Order Controllers for Delay Systems: Discrete Time Case

In this short paper we present-our preliminary results on the problem of finding fixed order stabilizing controllers for SISO discrete time finite dimensional plants. We assume that the controller has a computational time delay which increases with its dimension. This time delay is appended to the plant, and a fixed order stabilizing controller is investigated for the modified plant. We obtain necessary and sufficient conditions on the structure of fixed order controllers stabilizing a given plant with a time delay depending on the order of the controller.