Robust H∞ control for time-delay systems with additive controller uncertainty

This paper develops an H_∞ control technique for uncertain linear time-delay systems, which takes account of not only plant uncertainty but also controller uncertainty. Considering additive controller gain variations, the paper focuses on the design of memoryless state feedback control such that the closed-loop system is quadratically stable and possesses an H_∞ disturbance attenuation bound for all admissible uncertainties and arbitrary unknown delay. With the assumption that all the plant and controller uncertainties are described by time-varying but non-bounded form, the design method is presented based on algebraic Riccati inequality, and furthermore the obtained results can be transferred to the LAB problem based on Schur complements.