Distributed Stability Tests for Large-Scale Systems with Limited Model Information

Privacy concerns spark the desire to analyze large-scale interconnected systems in a distributed fashion, that is, without a central entity having global model knowledge. Two different approaches are presented to analyze the stability of interconnected linear time-invariant systems with limited model knowledge. The two algorithms implement sufficient stability conditions and require information exchange only with direct neighbors thus reducing the need to share model data widely and ensuring privacy. The first algorithm is based on an M-matrix condition, and the second one is based on Lyapunov inequalities. Both algorithms rely on distributed optimization using a dual decomposition approach. Numerical investigations are used to validate both approaches.