Integral quadratic constraint approach vs. multiplier approach

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. Using a slightly modified multiplier approach, we show that the existence of an IQC is equivalent to the existence of a multiplier in most known cases. It is hoped that this result provides some new insight into both approaches and makes them more useful in robust control applications.