Coprime Inner/Outer Factorization of SISO Time-Delay Systems and FIR Structure of Their Optimal H-Infinity Controllers

The approach in Foias et al. (1996) is one of the well-developed methods to design H-infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime inner/outer factorization. We give the largest class of single-input-single-output (SISO) time delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H-infinity performance and eliminate unstable pole-zero cancellations in the optimal H-infinity controller. We extend the results on the finite impulse response (FIR) structure of optimal H-infinity controllers by showing that this structure appears not only for plants with input/output (I/O) delays, but also for general SISO time-delay plants.