Coprime-inner/outer factorization of SISO time-delay systems and FIR structure of their optimal H-infinity controllers

The approach in Foias et al. (Robust control of Infinite Dimensional: Frequency Domain Methods. Springer: Berlin, 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-inputsingle-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 structure of optimal H-infinity controllers by showing that this structure appears not only for plants with input/output delays, but also for general SISO time-delay plants. Copyright (c) 2011 John Wiley & Sons, Ltd.