IQC Toolbox: A MATLAB Toolbox for Robust Stability and Performance Analysis. Engineers typically base their work on mathematical models of actual processes. The mathematical models rarely describe the real processes accurately and could behave quite differently from the real process. Hence, the post-design analysis on the system’s performance and robustness becomes an important stage in any engineering process. Performance analysis is often done by computer simulation. However, for systems with infinite dimensional uncertainties (e.g. uncertain time delay), it is unlikely to explore all possible behaviors of the real system by simulation. For engineering systems with high quality requirements, such as aircraft control systems and high speed elevators, more rigorous and efficient analysis approaches are desirable. Robust stability and performance analysis have been active topics in the field of systems and control theory because of their practical importance. A variety of approaches have been developed since the 1940s. Many of these analysis methods are, explicitly or implicitly, based on a concept called ”Integral Quadratic Constraint” (IQC). In this paper, we consider robustness analysis of complex systems using the IQC framework. We start with a brief introduction to the most basic ideas behind the IQC framework. Then we present a MATLAB toolbox which is built for performing analysis based upon this idea.