Integral quadratic constraint approach vs. multiplier approach

Abstract

Integral quadratic constraints (IQC) arise in many optimal and/or robust control problems. The IQC approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory. In this paper, we study the relationship between the two approaches for robust stability analysis. The key result shows that for many applications, the existence of an IQC is equivalent to the existence of a multiplier. Because the multiplier approach is typically simpler and more intuitive, this result suggests that the multiplier approach may be more useful than the IQC approach in many applications.