In this report, we investigate the performance analysis of uncertain large scale systems. Due to their complexity, the usual robustness analysis methods based on e.g: $\mu$ or Integral Quadratic Constraints (IQC) cannot be practically applied. In order to address this problem, in [1], we propose to represent a large scale system as an interconnection of sub-systems and to perform a hierarchical analysis by propagating the IQC characterization of each uncertain sub-system through the interconnection. For a given computational time, the conservatism of the analysis dramatically depends on the class of IQC under consideration. In this report, we propose a new class of IQC which characterizes the phase of uncertain system. An application to the robustness analysis of a PLL network reveals that the use of this class of IQC improves the trade-off between conservatism and computation time.