This paper investigates the performance analysis of uncertain large scale systems. Due to their complexity, the usual robustness analysis methods based on e.g; µ or Integral Quadratic Constraints cannot be practically applied. In order to address this problem, in [1], we propose to representa 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 paper, we propose a new class of IQC which characterizes the phase of uncertain system. An application to the robustness analysis of a PLL network reveal that the use of this class of IQC improves the trade-off between conservatism and computation time.