Phase IQC for the hierarchical performance analysis of uncertain large scale systems

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 (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 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 reveals that the use of this class of IQC improves the trade-off between conservatism and computation time.