Coalitional Control: Clustering Based on the H₂ Norm

This work presents an original analysis of the coupling sources in a network of dynamical systems. A coalitional controller exploits switching between different groupings of network members to achieve its regulation goals. In this work, we rigorously analyse a key assumption in robust distributed control methods: the weak coupling assumption. We present an analysis based on Linear Matrix Inequalities to assess this assumption to design Robust Control Invariant sets for all possible network partitions. We also exploit our coupling analysis to propose a novel partition selection optimisation based on the system’s H2 norm. This strategy simplifies the partition selection process, as demonstrated through illustrative examples, leading to enhanced computational efficiency while rigorously preserving the stability and robustness essential for distributed control system applications.