Convex Hierarchical Analysis for the Performances of Uncertain Large-Scale Systems

The performance analysis of uncertain large-scale systems is considered in this paper. It is performed via a hierarchical modelling and analysis of the systems thanks to the recursive application of a propagation of dissipativity properties result. At each step of the analysis, the local part of the system is viewed as the interconnection of sub-systems. The propagation is used to obtain 'propagated' dissipativity properties of this local part from 'sub' dissipativity properties of the sub-systems. At the next step, the former 'propagated' porperties are used as 'sub' properties. This is in contrast with an one-step approach such as (upper bound) µ-analysis hich computation time can be prohibitive for large-scale systems even if the associated optimization problem is convex: the trade-off between conservatism and computation time is not necessarily adapted. The purpose is then to obtain a trade-off suited to large-scale systems, an interesting feature being that the trade-off can be set by the user. The approach is used on a PLL network example and illustrates the new trade-off achieved