A four-block problem for H∞ design: properties and applications

A four-block H_∞ optimal control problem is studied from the point of view of its usefulness as a control system design tool. The problem is a natural generalization of several H _∞ optimal control problems, e.g., mixed sensitivity and gap/normalized-coprime-factor optimization. The problem is well posed in the sense that the optimal performance depends continuously on the plant, where perturbations are measured in the gap metric. Two design examples are presented. In the first, the problem is used to solve a weighted sensitivity minimization problem for a plant with poles and zeros on the stability boundary. In the second, a flexible structure design, in which both performance and robustness goals are specified, is carried out