A decomposition approach to distributed analysis of networked systems

We present a simple distributed algorithm for analyzing well-posedness and stability of a system composed of different sub-units, interconnected over an arbitrary graph. The procedure consists in solving a set of coupled linear matrix inequalities via a subgradient method, with primal decomposition. The proposed algorithm can be implemented in parallel on the system's graph and should prove more efficient than conventional semidefinite programming solvers, for very large systems with a high number of states and interconnection variables.