Input-to-Output Stability and Consensus Control of Opinion Dynamics on Graph State-Space

This paper proposes a modeling of opinion dynamics in social systems with evolving structures on the Graph State-Space. It builds upon the Hegselmann-Krause (HK) model with variable influence weights, integrated into a hybrid dynamical systems framework where structural changes (agent addition/removal) are induced by inputs. We establish an Inputto-Output Stability (IOS) result under a strong connectivity assumption, using a nonsmooth Lyapunov function based on the opinion diameter; we show that the consensus expansion is then bounded by the maximal deviation of incoming agents relative to the existing convex hull. Assuming constant influence weights, we propose a consensus control result via agent injection in the social system. The results of this paper initiate, to the best of our knowledge, the analysis of resilience, stability, and control of dynamic systems on Graph State-Space.