Coprime‐inner/outer factorization of SISO time‐delay systems and FIR structure of their optimal<i>H</i>‐infinity controllers

Abstract

SUMMARY 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‐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 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 © 2011 John Wiley &amp; Sons, Ltd.