A discrete-time doubly coprime factorization based on the predictor-based LQG controller

Abstract

Based on the predictor-based LQG controller, we derive a state-space representation of a discrete-time doubly coprime factorization. This representation can easily be obtained by applying standard numerical methods for a state-space model of a plant. We find a simple relation between the factorizations for different delays. Then we propose a simple and convenient parameterization of all stabilizing controllers under general feedback delays. By this parametrization, we can easily apply various new design techniques, which are usually proposed for continuous-time systems, to discrete-time systems under general feedback delays. As an application, we discuss loop transfer recovery using the free parameter in the proposed parametrization.