Compositional stability analysis based on dual decomposition

We propose a compositional stability analysis framework for verifying properties of systems that are interconnections of multiple subsystems. The proposed method assembles stability certificates for the interconnected system based on the certificates for the input-output properties of the subsystems. The decomposition in the analysis is achieved by utilizing dual decomposition ideas from optimization. Decoupled subproblems establish subsystem level input-output properties whereas the "master" problem imposes and updates the conditions on the subproblems toward ensuring interconnected system level stability properties. Both global stability analysis and region-of-attraction analysis are discussed.