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A Hierarchical Approach to Stability Assessment of Large Scale Interconnected Networks

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified model of linear interconnection of linear subsystems, where provably global properties, e.g. global convergence to a specific state, usually hold true. However, in severely disturbed conditions many of those systems exhibit strongly nonlinear behaviour. Particularly, multiple equilibrium points may coexist and make the dynamical behavior of the system difficult to predict. Aiming at understanding the fragility of interconnected systems, we will provide a hierarchical framework to assess the metastability and resilience of such systems. This framework is based on independently characterizing stability of individual subsystems when they are uncoupled from the network, and then enforcing the diagonal dominance property on a structure matrix capturing the subsystems stability and the input-to-output gains of interconnection network. Since the subsystems are usually of low order and the structure matrix has size equal to the number of subsystems, this framework is easy to implement and thus scalable to large scale interconnected systems. Possible application of this framework in assessing stability of microgrids will be discussed at the end of this paper.