  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.
